(D) The equation of the circle is $x^2 + y^2 = 16$,which has center $(0, 0)$ and radius $r = \sqrt{16} = 4$.For the line $y = mx + c$ to touch the cir

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(D) The equation of the circle is $x^2 + y^2 = 16$,which has center $(0, 0)$ and radius $r = \sqrt{16} = 4$.For the line $y = mx + c$ to touch the circle $x^2 + y^2 = r^2$,the condition is $c^2 = r^2(1 + m^2)$.Here,$m = \sqrt{3}$,$c = k$,and $r = 4$.Substituting these values,we get $k^2 = 4^2(1 + (\sqrt{3})^2)$.$k^2 = 16(1 + 3) = 16 \times 4 = 64$.Therefore,$k = \pm 8$.

Class 11 Mathematics 10-1.Circle and System of Circles Tangent and normal to a circle

Medium

If the line $y = \sqrt{3}x + k$ touches the circle $x^2 + y^2 = 16$,then $k =$

A
$0$
B
$2$
C
$4$
D
$\pm 8$

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10-1.Circle and System of Circles

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Tangent and normal to a circle

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If the line $y = \sqrt{3}x + k$ touches the circle $x^2 + y^2 = 16$,then $k =$

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