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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 x2a2+y2b2=1\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 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.