A conic satisfies the differential equation and passes through the point

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Calculus · Calculus

Problem

A conic

C

satisfies the differential equation

(1+y^2)\,dx - xy\,dy = 0

and passes through the point

(1,0)

. An ellipse

E

which is confocal with

C

has its eccentricity equal to

\sqrt{\frac{2}{3}}

. Find the locus of the point of intersection of the perpendicular tangents to the ellipse

E

. (1)

x^2 + y^2 = 4

(2)

x^2 + y^2 = 8

(3)

x^2 + y^2 = 10

(4)

x^2 + y^2 = 13