Question
Question: If PCP' and DCD' be a pair of conjugate diameter of an ellipse \(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{...
If PCP' and DCD' be a pair of conjugate diameter of an ellipse a2x2+b2y2=1 whose centre is C then (CP)2 + (CD)2 equals.
A
a2 + b2
B
(a2 - b2)2
C
(a + b)2
D
None
Answer
a2 + b2
Explanation
Solution
Coordinates of P and D are (α cosθ, b sinθ) and
{a cos (90 + θ), b sin (90 + θ)}
∴ CP2 + CD2 = (a2 cos2θ + b2 sin2θ) + (a2 sin2θ + b2 sin2θ).
= a2 + b2.