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P is a variable point such that the two tyangents drawn to the ellipse x 2 /a 2 +y 2 /b 2 =1 from the point P are perpendicular to each other.Find the equation of locus of P.

P is a variable point such that the two tyangents drawn to the ellipse x2/a2+y2/b2=1 from the point P are perpendicular to each other.Find the equation of locus of P.

Grade:12th pass

1 Answers

Arun
25758 Points
3 years ago
Dear student
 
equation of tangents =
 
 y = mx ± sqrt (a^2 m^2 – b^2)
 
Now
 
make this in quadratic in m and then 
use relation m1 * m2 = – 1
 
hence you can find locus

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