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If $\frac{x}{a} + \frac{y}{b} = 1$ intersects $5 x^{2} + 5 y^{2} + 5 b x + 5 a y - 9 a b = 0$ at P and Q, $∠ P O Q = π / 2$ 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

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detailed solution

Correct option is B

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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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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Ready to Test Your Skills?

free study material

If $\frac{x}{a} + \frac{y}{b} = 1$ intersects $5 x^{2} + 5 y^{2} + 5 b x + 5 a y - 9 a b = 0$ at P and Q, $∠ P O Q = π / 2$ then the relation between a and b is