First slide

Pair of straight lines

Question

The angle between the pair of straight lines formed by joining the points of intersection of $x^{2} + y^{2} = 4$ and $y = 3 x + c$ to the origin is a right angle. Then $c^{2}$ is equal to

Moderate

Solution

$\frac{y - 3 x}{c} = 1$
$x^{2} + y^{2} - 4 {(1)}^{2} = 0; x^{2} + y^{2} - 4 {(\frac{y - 3 x}{x})}^{2} = 0$
$\begin{array}{l} a + b = 0 \\ c^{2} = 20 \end{array}$

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