0
votes
2answers
36 views

How to show that a given line has a certain equation?

Say line $A(3,0)$ and $B(0,2)$ How do I 'show' that they have equation $2x + 3y - 6 = 0$?
1
vote
1answer
40 views

Show an equation of a line passing through $P$ and parallel to the line given by $ax+by+c=0$.

Question: A person considers lines on the plane $\mathbb{R^2}$ to be solutions of equations of the form $ax+by+c=0$, where $a,$ $b,$ and $c$ are fixed reals satisfying $a^2+b^2\neq0$. Give a point ...
1
vote
1answer
25 views

Line not intersecting circle, maximum value of expression involving radius

If line $y+x=2$ do not intersect any member of circles $x^2 + y^2 -ax = 0$ at two distinct points where a is parameter, then maximum value of $|a + 4|$. My try: Since the line does not intersect ...
1
vote
2answers
103 views

Omitting $i$ in calculations

Is it possible in various calculations related to the complex plane which also include analytic geometry , calculating distances etc, to omit $i$ and treat the imaginary axis as simply the cartesian ...
1
vote
1answer
69 views

Equation of parabola, tangent at vertex [closed]

Two tangents on a parabola are $x-y=0$ and $x+y=0$. If $(2,3)$ is the focus of the parabola, then find the equation of tangent at the vertex. Thanks. My thoughts: Can't figure out anything :(
-1
votes
4answers
53 views

Find the line through $(-1,4)$ for which the distance to $(6,3)$ is 5

This is the question: Find the line through $(-1,4)$ for which the distance to $(6,3)$ is $5$ The answer is: $y-4=-4/3(x+1)$ and $y-4=3/4(x+1)$ I do not know how to get this answer. ...
1
vote
1answer
80 views

How can I convert the following parametric equation to cartesian equation?

\begin{align} x&=\left(1 + \frac{1}{\,\sqrt{\,2t^{2} - 4t + 4\,}\,}\right)t\ -\ 2 \\[3mm] y&=\left(1 - \frac{1}{\,\sqrt{\,2t^{2} - 4t + 4\,}\,}\right)t\ +\ \frac{2}{\,\sqrt{\,2t^{2} - 4t + ...
0
votes
2answers
63 views

How do i Solve the Radius of the circle?

Hello I was wondering about this kind of problem I'm having. Here it is: $$ x^2 + y^2 = 49 $$ Formula given by our instructor is: $x^2 + y^2 = r^2$.
3
votes
1answer
55 views

Given an ellipse's center, focus and point, find its equation.

Given an ellipse's center is $(2,1)$, focus is (2,4) and point is (3,-3), we have Plug in center: $\frac{(x-2)^2}{a^2}+\frac{(y-1)^2}{b^2} = 1$ Use focus: $4^2=a^2-b^2$ $16=a^2-b^2$ Use point: ...
1
vote
0answers
28 views

Given equation of parabola, find vertex and directrix

Given that $x^2-bx+17-ay=0$ has vertex $(3,2)$, find the directrix and focus. My attempt is to make it into the form $(x-h)^2=4a(y-k)$ which has focus $(h,k+a)$ and directrix $y=k-a$. Is this right? ...
0
votes
4answers
593 views

Finding an equation of circle which passes through three points

How to find the equation of a circle which passes through these points $(5,10), (-5,0),(9,-6)$ using the formula $(x-q)^2 + (y-p)^2 = r^2$. I know i need to use that formula but have no idea how to ...
1
vote
3answers
96 views

Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
1
vote
1answer
56 views

Finding the intersection of a circle and a line

The text says: On a single set of coordinate axes, sketch the line $x+16 = 7y$ and circle $x^2+y^2-4x+2y=20$ and find their points of intersection. Hint: eliminate x algebraically and solve the ...
0
votes
1answer
25 views

Equation of line passing through a point parallel to a given line

I have the point $(2,-5)$ and an equation $y-4 = 2x$ which is a straight line. I want to make another equation from the $(2,-5)$ that is parallel to $y-4 = 2x$ and you can only do this by making the ...
0
votes
2answers
52 views

Hyperbolas - Standard Form

This is probably a simple question but if $y = \frac{1}{x}$ is a hyperbola, then how does it comply with the standard form of a hyperbola?
1
vote
1answer
42 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
30 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
41 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
25 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 ...
8
votes
4answers
264 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
54 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
89 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
555 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
69 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
4answers
126 views

How do I find the center and radius of this circle? [closed]

How do I find the center and radius of this circle? $$4x^2+4y^2+24x-16y+41=0$$
0
votes
1answer
266 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
114 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
92 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
783 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
341 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
57 views

Finding Coordinates of sphere [closed]

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
81 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 ...
0
votes
2answers
479 views

Linear equations; how to write an equation from given coordinates?

A straight line goes through the points $( 0, 1 )$, $( 2, 7 )$ and $( 4, 13 )$ and I need to write the equation of this straight line. How do you write equations? I know you have it's usually $y = x ...
-1
votes
1answer
146 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
71 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
48 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
153 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
210 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
246 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
144 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
133 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
48 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
79 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
50 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
155 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
280 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
608 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 ...