if the chord of contact of tangents from two points (x1,y1) an d (x2,y2) to the ellipse x2 + y2= - Maths - Continuity and Differentiability

Question

if the chord of contact of tangents from two points (x1,y1) an d
(x2,y2) to the ellipse x2 + y2= 1 are at
right angles , then x1x2/y2y1 is equal to -
a4/b4 prove this

Rahul Raj · Accepted Answer

dear student

the equation of chord of contact from (x1,y1) to the ellipsex2a2+y2b2=1isxx1a2+yy1b2=1so in this case two lines arexx1a2+yy1b2=1xx2a2+yy2b2=1as two lines are perpendicularso product of slopes = -1-b2x1a2y1-b2x2a2y2=-1sox1x2y1y2=-a4b4

regards

if the chord of contact of tangents from two points (x1,y1) an d (x2,y2) to the ellipse x2 + y2= 1 are at right angles , then x1x2/y2y1 is equal to - a4/b4. prove this

if the chord of contact of tangents from two points (x1,y1) an d (x2,y2) to the ellipse x² + y²= 1 are at right angles , then x1x2/y2y1 is equal to - a⁴/b⁴. prove this