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Tangent To a Parabola

If the line ...

Question

If the line $y = 2 x + c$ is a tangent to the circle $x^{2} + y^{2} = 5$ , then a value of $c$ is

- 5

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3

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Solution

The correct options are
B $- 5$
C $5$
Given equation of line is $y = 2 x + c$ and equation of circle is $x^{2} + y^{2} = 5$
For given line to be tangent its distance from center must be equal to radius of the circle
$\Rightarrow \frac{| c |}{\sqrt{4 + 1}} = \sqrt{5}$
$\Rightarrow c = \pm 5$

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