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Q.

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 c² is

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a

$\frac{1}{5}$

b

13

c

20

d

5

answer is A.

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Detailed Solution

Homogenising the equations we get

$x^{2} + y^{2} - 4 {(\frac{y - 3 x}{c})}^{2} = 0$

The angle made $= \frac{π}{2}$

$\Rightarrow coefficient of x^{2} + coefficient of y^{2} = 0$

$\begin{array}{l} 1 - \frac{36}{c^{2}} + 1 - \frac{4}{c^{2}} = 0 \\ \Rightarrow 2 c^{2} = 40 \end{array}$

and so $c^{2} = 20$

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