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Definition of Hyperbola

If h2+k2>a2...

Question

If $h^{2} + k^{2} > a^{2}$ , then the number of solutions of the equation $h x + k y = a^{2}$ and $x^{2} + y^{2} = a^{2}$ is

1

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2

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4

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0

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Solution

The correct option is B $2$
$x^{2} + y^{2} = a^{2}$
Given $h^{2} + k^{2} > a^{2}$
then $p (h, k)$ lies outside circle $x^{2} + y^{2} = a^{2}$
Then chord of contact from $p (h, k)$ to $x^{2} + y^{2} = a^{2}$ is
$x h + y k = a^{2}$
So, $x h + y k = a^{2}$
$\Rightarrow$ no. of solution of the equation $h x + k y = a^{2}$ and $x^{2} + y^{2} = a^{2}$ are $2.$

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