If xa+yb=1 intersects 5x2+5y2+5bx+5ay−9ab=0 at P and Q, ∠POQ=π/2 then the relation between a and b is

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a = b

a = 2b or b = 2a

a = 3b or b = 3a

a + b = 5

answer is B.

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Detailed Solution

Homogenising, 5x2+5y2+(5bx+5ay)xa+yb−9abxa+yb2=0coefficient of x2 + coefficient of y2⇒5+5ba−9ba+5+5ab−9ab=0⇒b(5a−4b)+a(5b−4a)=0⇒(a−2b)(2a−b)=0

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