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A pair of perpendicular lines passed through the origin and also through the point of intersection of the curve $x^{2} + y^{2} = 4$ with the line $x + y = a$ . The set containing the value of ‘a’ is ____

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$\{2, - 2\}$

$\{- 3, 3\}$

$\{- 4, 4\}$

$\{- 5, 5\}$

answer is A.

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Detailed Solution

$x^{2} + y^{2} = 4$ and $x + y - a = 0$

Homogenise $x^{2} + y^{2} - 4 {(\frac{x + y}{a})}^{2} = 0$

$\bar{O A} ⊥ \bar{O B} \Rightarrow 1 - \frac{4}{a^{2}} + 1 - \frac{4}{a^{2}} = 0$

$2 = \frac{8}{a^{2}}$

$\Rightarrow a = \pm 2$

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