All Questions
Tagged with geometry analytic-geometry
2,579
questions
2
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53
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Find the vertices of a non-canonical hyperbola
Given the hyperbola
$$x^2+6xy-7y^2=20,$$ how do I find its vertices? I have found its asymptotes by factoring it into $$(x+7y)(x-y)=20$$ to obtain its asymptotes: $$y=x$$ and $$y=-\frac{1}{7}x.$$ I do ...
- 31
0
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0
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36
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Solution suggested to "Distance from a point to a plane" problem in test might be wrong
This is from an application exam. What you see in the image is the answer they gave for a question I disagree with.
My answer is $\frac{10}{3}$ using $$\text{Distance}=\frac{\left|A x_0+B y_0+C z_0+...
- 413
2
votes
1
answer
93
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Finding center of rotation on a plane using complex numbers
Let $V_1$ be the anti-clockwise rotation in the plane about origin with $\theta$ angle and $V_2$ be the anti-clockwise rotation in the plane about (2,0) by $\theta$ angle. finding its center of ...
- 368
3
votes
6
answers
230
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Rotating and scaling an arbitrary triangle such that the new triangle has its vertices on the sides of the original one
Given $\triangle ABC$, and a scale factor $r \lt 1 $, I want to find the necessary rotation (center and angle) such that the rotated/scaled version of the triangle has its vertices lying on the sides ...
- 24.2k
3
votes
3
answers
167
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How can I fit a circle into the gap between an ellipse and the coordinate axes?
Consider an ellipse with the equation $\frac{\left(x-ar\right)^{2}}{a^{2}}+\frac{\left(y-br\right)^{2}}{b^{2}}=r^{2}$. How would I fit a circle with an equation $\left(x-k\right)^{2}+\left(y-k\right)^{...
- 35
2
votes
3
answers
220
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Range for radius of tangent sphere to three given spheres
You're given three spheres of radii $a, b, c$ where $a \le b \le c $. The three spheres are placed on a table (represented by the $xy$ plane), such that they tangent to each other. I want to find ...
- 24.2k
-1
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2
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63
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If we spin an ostrich egg along its minor axis will it be oblate shape?
An ostrich egg is classified as an ellipsoid and if we spin it around it's major axis it's classified as a prolate but my fried is arguing that we can not spin that ellipsoid around its minor axis ...
1
vote
1
answer
29
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How to modify off-center circle in polar coordinates so that input angle has a linear relationship with angle on circle?
I have a circle translated horizontally in polar coordinates described by the equation:
$$r\left(\theta\right)=d\cos(\theta)+\sqrt{r_{0}^{2}-d^{2}\sin^{2}(\theta)}$$
where $d$ is the horizontal ...
- 13
3
votes
3
answers
243
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Inscribing two circles and an ellipse in a square
A square of given side length $S$ is to inscribe two circles and an ellipse as shown in the figure below.
If the radius of circle $(1)$ is given, determine the center and radius of circle $(2)$, then ...
- 24.2k
6
votes
4
answers
336
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Rolling an elliptical disc on the $x$ axis
You're given the elliptical disc bounded by
$ \dfrac{x^2}{a^2} + \dfrac{(y - b)^2}{b^2} = 1 $
where $a = 5, b = 2 $. You roll this ellipse to the right along the positive $x$ axis, such that it is ...
- 24.2k
0
votes
0
answers
45
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Angle between two lines in 3D geometry
I have the following problem:
Find the lines parallel to the plane $\pi: y+\sqrt[2][2]z-1=0$ and which form an angle of $\pi/3$ with the x axis
I would like to start by posing the problem as follows:
-...
- 75
6
votes
3
answers
453
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Find the radius of the red circle
Four circles are arranged as shown in the figure below. They're numbered from $1$ to $4$.
If the diameter of circle $C_2$ is equal to $9$, and $ PT = 6 , QT = 3 \sqrt{5} $. It is also given that $UV ...
- 24.2k
0
votes
0
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40
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Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at the point $E$ outside the circle. Prove that
(a) $\angle A\cong\angle C$
(b) $\angle1\cong\angle 2$
(c) $\triangle ADE$ and $\triangle CBE$ are equiangular.
I tried upto some extent but did not know I to solve this problem.
I know that length ...
- 602
0
votes
1
answer
47
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Determine Intersection Point Quadratic Bezier Curve and Plane
I need to compute the intersection point between a quadratic bezier curve and a plane. Thereby i have to solve the equation for the parameter t. The normal vector is in the dot product to the square ...
- 3
-2
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1
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50
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Finding the equations of the lines tangent to $Ax^2+2Bxy+Cy^2+2Dx+2Ey+F=0$ and parallel to $Gx+Hy+I=0$ [closed]
A curve $Ax^2+2Bxy+Cy^2+2Dx+2Ey+F=0$ and a line $Gx+Hy+I=0$ are given. How do I find the equation of the tangent (tangents) to a given curve that is (are) parallel to a given line?
