1
vote
1answer
20 views

Check my solution to this trig inequality

Problem $1.88$ : Solve $$\cos x\lt \frac{\sqrt{3}}{2},\qquad x \in [0,2\pi]$$ I found the set of solutions to be $S=[0,2\pi]-\left[\dfrac{\pi}{6},\dfrac{11\pi}{6}\right]$ Is this correct? Thank you.
1
vote
1answer
24 views

need explanation of what exactly is a directrix & focus?

((I'm not asking why do we need to know conic sections etc.) Like other similar questions.) I actually love math & currently learning conic sections in class, neither my textbook or teacher ...
1
vote
2answers
37 views

Finding root for the segment - found the formula but it doesn't work for some values - wrong formula?

I have the segment, defined as $(x_1, y_1)$, $(x_2, y_2)$. I know that $y_1\ge 0$ and $y_2 < 0$. I want to compute the root point for that segment. I decided to do it that way: ...
-1
votes
1answer
20 views

Graph a line oriented by an specific angle?

I'm writing a software that plots gps data on a map, and so far it has been riddled with complex math problems, many of which I was able to fix by myself but this one I can't figure out. The software ...
9
votes
4answers
170 views

Can we plot a regular octagon on a set of axes, where all vertices of the octagon lie on integer co-ordinates?

I'm a high school teacher and someone asked me this in my class, and to be honest I'm quite stumped! I haven't done any high level math in such a long time, and I'm really not sure how to approach ...
1
vote
1answer
50 views

Product of gradients of x=0 and y=0

A friend asked me this question: The product of the gradient of any two lines perpendicular to each other is $-1$. Now, the lines $x=0$ and $y=0$ are perpendicular to each other. If you take the ...
0
votes
2answers
83 views

Find the equation defining a perpendicular bisector

Hello fellows, I've not had much time to post questions, but I post this one because while in my Maths lesson, I became annoyed by solving the same thing over and over again, when a good ...
1
vote
1answer
226 views

Intersection of a plane with an infinite right circular cylinder by means of coordinates

So, I started studying analytic geometry and I must say I'm finding it much harder than "classic" geometry, because of the equations without help from diagrams... Still, I wanted to see how to use it ...
2
votes
1answer
53 views

Product of the distance from foci to a tangent is a constant

I am supposed to determine what is the result of said product. Given $P(x_0,y_0)$, I need to calculate the distance from the foci to the tangent line that passes through $P$, and then multiply the ...
0
votes
1answer
217 views

Intersection of two planes and another plane parallel to the intersection.

I have two questions: $1)$ How can I find the line of intersection between the planes $$x+ 2y +z =4 \\ \mathrm{and} \\ 2x+y-z=5$$ $2)$ How do I find an equation for a line that goes through $A = ...
3
votes
1answer
91 views

Parabolas intersecting in integer points

Can you construct an example of two different parabolas (with integer coefficients) that intersect at three integer points? An integer point is a point $(x,y)$ where both $x$ and $y$ are integers.
1
vote
0answers
79 views

Draw the locus of points which satisfy the equation

(1) Draw the locus of points $(x,y)$ which satisfy the following equation. $bx^{3}+y^{3}+x^{2}y+bxy^{2}-4abxy-2ab^{2}x^{2}-2ay^{2}+b\left( a^{2}b^{2}+a^{2}-1\right)x+\left( a^{2}b^{2}+a^{2}-1\right) ...
2
votes
1answer
452 views

Convert two points to line eq (Ax + By +C = 0)

Say one has two points in the x,y plane. How would one convert those two points to a line? Of course I know you could use the slope-point formula & derive the line as following: $$y - y_0 = ...
0
votes
1answer
276 views

finding the coordinates of a point of intersection: 3d sphere and plane [duplicate]

How to find the coordinates of one point on the interaction of the sphere $$(x-1)^2+(y-2)^2+(z-4)^2= 25$$ and the plane $z=4$. I was trying to solve this I got it down to $x+y=8$ but then when I ...
-3
votes
1answer
53 views

Finding Coordinates of sphere

Find the coordinates of one point on the intersection of the sphere $$(x-1)^2+(y-2)^2+(z-4)^2=25$$ and the plane $$z=4.$$ Supply evidence to support your answer.
2
votes
4answers
71 views

describe the domain of a function $f(x, y)$

Describe the domain of the function $f(x,y) = \ln(7 - x - y)$. I have the answer narrowed down but I am not sure if it would be $\{(x,y) \mid y ≤ -x + 7\}$ or $\{(x,y) \mid y < -x + 7\}$ please ...
-1
votes
1answer
130 views

Solve a parabola problem?

So, two parabolas are given: $y^2=24x$ and $x^2=3y$ and a point $A(24,3)$. If B and O are intersect points of these two parabolas, prove that the angle ABO is right.
1
vote
1answer
59 views

Understanding the graph of the displacement of a particle wirh respect to time

At time $t=0$ the position of the particle is $3 ft$, and at time $t=2$ the position of the particle is $11ft$. At time $t=0$ the velocity of the particle must have been zero. So if its the motion ...
1
vote
2answers
46 views

Slope of a straight line

Why is this so that a higher value of slope indicates a steeper incline? I can't take it into my head. What could be the reason behind that? I know that it is a fact because I've also noticed it but ...
0
votes
1answer
105 views

In an equation that looks like the standard form of an ellipse, what must the constant on the RHS equal for exactly one solution?

I am working on a homework question: What must be the value(s) of $c$ for the following equation to have exactly 1 solution? The equation is of the standard form of the equation for an ellipse, ...
1
vote
3answers
202 views

Area Between Curves

The problem I am working on is, "In Exercises 17 and 18, find the area of the region by integrating (a) with respect to and x (b) with respect to y." The two functions: $g(y)=4-y^2$, and $f(y)=y-2$ ...
1
vote
2answers
211 views

Parametric Equation Problem

The problem is, "to determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain." (a) $x=t;\quad ...
1
vote
1answer
119 views

Restriction Of Parametric Functions Domain

The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the ...
2
votes
1answer
112 views

Sketching A Plane Curve

The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the ...
0
votes
6answers
47 views

Finding the slope of a function

How do I find the slope of this function: $px + (2p-1)y + 4 = 0$ I need to know how to answer a previous question of mine (also posted on this forum)
0
votes
5answers
74 views

Determine a parameter in such a way that two lines are parallel

The lines $px + (2p-1)y + 4 = 0$ and $(p+3)x + 2py + 6 = 0$ are parallel to each other. Find $p$. I have no idea how to tackle this problem, can anyone help?
0
votes
3answers
70 views

Mathematical 'language' (geometry)

What does this question mean: 'Show (translated from my native language) that the equation $ x^2 - 4x + y^2 + 6y = 51 $ is a circle.' I have absolutely no idea how to 'show/prove/etc.' it, other than ...
1
vote
2answers
47 views

An analytic geometry question + algebra

We have a Cartesian coordinate system with the points M (a,b) Q (4,2) and P (x,y) but I don't think you need P to solve this one, only M and Q. M is the middle of a circle with a radius r, and Q is a ...
0
votes
0answers
79 views

Eccentricity and Length of Semi Axes of a conic

If a conic $ax^2+by^2+2hxy+2gx+2fy+c=0$ and say: How to find the eccentricity and the semi-axes of this conic. I do understand that if its a hyperbola only one of the semi axes will be real. Soham
2
votes
1answer
154 views

How to constrain disks that intersection of them is inside unit circle

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ ...
1
vote
1answer
260 views

How to find intersection of an ellipse and a line that passes through the foci

There are two lines, parallel to the $x$-axis, which pass through the foci and intersect the ellipse at four points. How can I find the points of intersection? vertex: $(0,0)$ foci: $(0,10)$ and ...
1
vote
2answers
1k views

Mathematics behind intersection points of two lines using quadratic equation

This is the question I am trying to solve. I do not need any code examples just help on mathematics. Suppose two line segments intersect. The two endpoints for the first line segment are $(x_1, ...
3
votes
2answers
484 views

Intersection of two lines using general form

How do I find the intersection of these two lines with their equations in general form. I don't want to graph them and I'm wondering if its possible with out converting them to gradient intercept ...
0
votes
1answer
73 views

Vectors - For which value of t is the moving point A on $\vec{g}$ the closest to point B?

I'm having trouble finding a way to solve this particular problem: The point $A$ moves on $\vec{g}$ from point $J$ to $G$ and is dependent on the real parameter $t$: $\vec{g} = (-1/0/0) + ...
3
votes
3answers
6k views

Finding out whether two line (segments) intersect

I need to know whether or not two line segments intersect. I thought the formula for that is y = mx + b but I don't think that will work for what I need, at least I think I need to first know whether ...
1
vote
3answers
156 views

Finding any point on a line if you know the slope and $y$-intercept.

I am wondering if there is a way to determine where a point is if I only know the slope and $y$-intercept. For example, say I am told that the line has a slope of $3$ and a $y$-intercept of $-3$. ...
3
votes
3answers
140 views

What equation intersects only once with $f(x)=\sqrt{1-(x-2)^2}$

Being $f(x)=\sqrt{1-(x-2)^2}$ I have to know what linear equation only touches the circle once(only one intersection), and passes by $P(0,0)$. So the linear equation must be $y=mx$ because $n=0$. I ...
2
votes
3answers
400 views

How to fill up the gap between a typical advanced undergraduate algebraic curve course and High school basic geometry/precalculus course?

Based on this question i asked recently: A question about geometry of plane curve books, i think it is too advance for a HS student/ typical second or third year undergraduate math majors to read on ...
0
votes
1answer
33 views

Not very clear about “parametric form”

For example, let the surface $S$ in $\mathbb R^3$ be formed by taking the union of the straight lines joining pairs of points on the lines $$\{x=t,y=0,z=1\},\qquad \{x=0,y=1,z=t\}$$ with the same ...
1
vote
2answers
658 views

Finding & Plotting equation of hyperbola given foci, and difference in distances between them.

I have to plot the hyperbola (3 of them actually) in MATLAB, and so it'd be good if I could find some sort of general formula. The foci do not necessarily have to be on the axes (e.g. $(5,3)$ and ...
3
votes
2answers
5k views

How do I find the equation of a tangent line to a curve?

I'm given $x^2+2x-4$ at $x=2$ and I have to find the tangent line to this curve at that point...
2
votes
1answer
215 views

Need help with the proof of conic section

Prove that the intersection of a plane and a object consist of one cone and one upside-down cone where the tip of cone meet is either degenerate conic or conic Also, idenify in what situation, the ...
0
votes
2answers
98 views

Calculate Points for a Parallel Line

Given a line running through p1:(x1,y1) and p2:(x2,y2), I need to calculate two points such that a new parallel line 20 pixels away from the given line runs through the two new points. Edit: The ...
1
vote
1answer
178 views

questions from vectors applications

suppose that An boat captain wants to travel due south at 40 knots. If the current is moving northwest at 16 knots, in what direction and magnitude should he work the engine? here is given picture ...
1
vote
2answers
499 views

Finding the intersection of a two points and an arbitrary axis

Given two points I would like to find where the line joining them intersects an arbitrary axis. For example, if I had one point (5, 10) and another at (50, 100) I can be sure that somewhere a line ...
4
votes
4answers
1k views

Find the centre of a circle passing through a known point and tangential to two known lines

I am trying to find the centre and radius of a circle passing through a known point, and that is also tangential to two known lines. The only knowns are: Line 1 (x1,y1) (x2,y2) Line 2 (x3,y3) ...
1
vote
3answers
543 views

Find opposite vertices of a rhombus, given the other 2

I am stuck with this problem. I posted an earlier problem with a square, where rotation with i of 90 degrees was possible. This one is a rhombus, how should I proceed? Given ABCD is a rhombus with ...
2
votes
3answers
643 views

Simple gradient/line intersect question

Very, very basic question here: Given an x,y coordinate and a gradient (but no equation), how can I find the x and y axis intercepts? (assuming the line is linear)
9
votes
3answers
6k views

Equation of angle bisector, given the equations of two lines in 2D

I have two lines in 2D expressed with general equation (or implicit equation): First line: $a_1x+b_1y=c_1 \qquad(1)$ Second line: $a_2x+b_2y=c_2 \qquad(2)$ If the two lines are intersecting I will ...
0
votes
1answer
137 views

perpendicular distance to center of square from line in terms of slope

I am trying to find the relationship between the vertical distance (V) from the center of the square to the line to the perpendicular distance (P) from the center of the square to the line in terms of ...