The condition for a line $y = 2 x + c$ to touch the circle $x^{2} + y^{2} = 16$ is

c = 10

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c^{2} = 80

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c = 12

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c^{2} = 64

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Solution

The correct option is D $c^{2} = 80$
If $y = 2 x + c$ is a tangent

Radius = perpendicular distance from center to line

$r = \sqrt{16} = 4, C = (0, 0)$

$4 = \frac{| 0 - 0 + c |}{\sqrt{1^{2} + 2^{2}}}$

$c = 4 \times \sqrt{5}$

$c^{2} = 16 \times 5 = 80$

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The condition for a line y=2x+c to touch the circle x2+y2=16 is

The correct option is D c2=80If y=2x+c is a tangent Radius = perpendicular distance from center to line r=√16=4,C=(0,0) 4=|0–0+c|√12+22 c=4×√5 c2=16×5=80

The condition for a line $y = 2 x + c$ to touch the circle $x^{2} + y^{2} = 16$ is

The correct option is D $c^{2} = 80$
If $y = 2 x + c$ is a tangent

Radius = perpendicular distance from center to line

$r = \sqrt{16} = 4, C = (0, 0)$

$4 = \frac{| 0 - 0 + c |}{\sqrt{1^{2} + 2^{2}}}$

$c = 4 \times \sqrt{5}$

$c^{2} = 16 \times 5 = 80$