Problem 45315. Find the point of intersection of tangents.

Given two points on a conic, find the point of intersection of the corresponding tangents.
The conic is given in Cartesian coordinates by:
(1-e^2)*x^2 - 2*f*(1+e)*x +y^2 = 0
Where:
1. e is the eccentricity (assume e >=0). 2. f is the x coordinate of the focus which is in the half plane x >= 0.
The conic touches the y-axis at the origin. The foci are on the x-axis.
Additional information:
The conic is:
a. A circle if e = 0
b. An ellipse if 1 > e > 0
c. A parabola if e = 1
d. A hyperbola if e > 1
e. Degenerate if f = 0
Solve

Solution Stats

55.56% Correct | 44.44% Incorrect
Last Solution submitted on Feb 06, 2023

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