Tagged Questions
-1
votes
1answer
29 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
37 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 ...
0
votes
2answers
32 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
0answers
26 views
Distance functions
Lets consider three points $p_{0},p_{1},p_{2}$ and the coordinates are given by $(x_{0},y_{0},z_{0})$ , $(x_{1},y_{1},z_{1})$ and $(x_{2},y_{2},z_{2})$. Those three coordinates are given. Lets pick ...
0
votes
1answer
46 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
131 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
99 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
63 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
68 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
38 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
48 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
68 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
43 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
55 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
1
vote
1answer
110 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
683 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, ...
2
votes
2answers
158 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
66 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) + ...
2
votes
3answers
2k 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
77 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
110 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 ...
1
vote
3answers
268 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
31 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
413 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
2k 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
116 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
88 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
80 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
138 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
556 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
369 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
297 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)
6
votes
3answers
3k 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
106 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 ...
4
votes
2answers
587 views
Find equation for hyperbola
Just taking (failing) a simple algebra class, can't figure this one out and no one can explain it to me and the book just tells me to do it.
Find an equation for the hyperbola described:
foci ...
1
vote
1answer
60 views
Calculating gradient of a line: how do you know which way to order the points?
Very simple question but I keep getting this wrong!
If you have two points e.g. A$(13, 6$) & B$(11, 12)$,
Using the gradient formula $m = (y_2 - y_1)/(x_2 - x_1)$ how do you know which of A or B ...
5
votes
4answers
1k views
Why do rhombus diagonals intersect at right angles?
I've looked all over and I can't find a good proof of why the diagonals of a rhombus should intersect at right angles. I can intuitively see its true, just by drawing rhombuses, but I'm trying to ...
3
votes
2answers
489 views
Calculation of the touching point of two circles given limited data
I am trying to calculate the touching point of two circles. I have the following information.
Circle $1$:
Centre $(h,k)$
Radius $r_1$
Circle $2$:
Point on Circumference $(x_1,y_1)$
Radius ...
2
votes
4answers
224 views
Lines parallel to a given aline
I have to show that any line parallel to $Ax+ By + c =0$ is of the form $Ax + By + k =0$
How do I show this?
Thank you!
1
vote
4answers
286 views
Area of a quadrilateral
The perpendicular bisector of the line
joining A(0,1) and C(-4,7) intersects
the x-axis at B and the y-axis at D.
Find the area of the quadrilateral
Thank you in advance!
0
votes
7answers
687 views
Perpendicular bisector
"Show that BE is the perpendicular bisector to AC"
I tried to prove this through Pythagoras, but the answer I got did not prove it was at a right angle, and therefore said it was not the ...
2
votes
5answers
791 views
Cartesian Equation for the perpendicular bisector of a line
Find the Cartesian equation for the perpendicular bisector of the line joining A(2,3) and B(0,6)
How do I do this?
Thank you!
4
votes
1answer
1k views
Proving the Shoelace Method at the Precalculus Level
Using only precalculus mathematics (including that the area of the triangle with vertices at the origin, $(x_1,y_1)$, and $(x_2,y_2)$ is half of the absolute value of the determinant of the $2\times ...
