The angle between pair of lines joining $(0, 0)$ to the points of intersection of the curve $x^{2} + y^{2} = 9$ with the lines $x + y = 3$ is $\frac{π}{k}$ , then $k =$

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Solution

On homogenising $x^{2} + y^{2} = 9$ with $x + y = 3$
we have,
$x^{2} + y^{2} = 9 {(\frac{x + y}{3})}^{2} \Rightarrow x y = 0$
So this is the pair of lines joining $(0, 0)$ to the points of intersection of the curve $x^{2} + y^{2} = 9$ with the lines $x + y = 3$

Hence, the required angle between them is $= \frac{π}{2}$
$∴ k = 2$

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