0
votes
0answers
27 views

Conic equation from cone/plane intersection

In an orthonormal cartesian frame $(O; \vec{x}, \vec{y}, \vec{z})$ consider: an infinite plane $P$ defined by: a point $p = (p_x, p_y, pz)$ an normal vector $\vec{n} = (n_x, n_y, n_z)$ a cone $C$ ...
0
votes
0answers
50 views

Find points of intersection with cone on a plane at a given angles

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with ...
1
vote
3answers
106 views

How to find the point on a parabola where x and y are equal?

On a parabola how could i find the point at which the y and x points are equal and meet on a point of the graph, algebraically?
3
votes
2answers
218 views

2D point projection on an ellipse

I would like to find an equation to this problem: The problem is that I have an ellipse at a given center point C, with radius a (x axis), and radius b (y-axis). So far so good. Now I have the ...
17
votes
0answers
393 views

How many points of intersection between an ellipse and an $L_p$-circle?

Consider an ellipse $E$ in the plane, centered at the origin. (In my case, the minor axis points into the nonnegative quadrant.) Let S be an "$L_p$-circle": $S = \{(x,y) : |x|^p + |y|^p = 1\}$, ...
2
votes
1answer
192 views

proof that intersection of two conic sections will intersect at at least two points.

In the following equation $\rho(x,y)$ returns a constant value for a given coordinate. $\mathbf n$ is the normal vector to the surface of the form $[P,Q,-1]$ and $s$ is a direction vector. ...
0
votes
1answer
842 views

Find the intersection of a line (segment) and an ellipse (from the center of ellipse)

Here is what I know: The location of the center of the ellipse C (20,10). The Major axis (2a) or 400 (a being 200) - this is on the X axis. The Minor axis (2b) or 200 (b being 100) - on the y axis. ...
1
vote
1answer
533 views

Find intersection(s) between parametrized parabola and a line

I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...
0
votes
0answers
351 views

How to find intersections of hyperbolas by MATLAB

Let's have two hyperbolas given by equations: $$\mathbf{r}^T\cdot \mathbf A_1\cdot\mathbf r+\mathbf b_1^T\cdot\mathbf r+c_1=0$$ $$\mathbf{r}^T\cdot \mathbf A_2\cdot\mathbf r+\mathbf b_2^T\cdot\mathbf ...