The value of c,for which the line y = 2x + c | vedclass

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(C) The equation of the circle is $x^2 + y^2 = 16$,which is of the form $x^2 + y^2 = a^2$,where $a = 4$.The line $y = mx + c$ is a tangent to the circ

Vedclass · Accepted Answer

$4\sqrt{5}$

Vedclass · Answer

(C) The equation of the circle is $x^2 + y^2 = 16$,which is of the form $x^2 + y^2 = a^2$,where $a = 4$.The line $y = mx + c$ is a tangent to the circle $x^2 + y^2 = a^2$ if $c^2 = a^2(1 + m^2)$.Here,$m = 2$ and $a = 4$.Substituting these values,we get $c^2 = 4^2(1 + 2^2) = 16(1 + 4) = 16(5) = 80$.Therefore,$c = \pm \sqrt{80} = \pm 4\sqrt{5}$.Since $4\sqrt{5}$ is one of the given options,the correct value is $4\sqrt{5}$.

The value of $c$,for which the line $y = 2x + c$ is a tangent to the circle $x^2 + y^2 = 16$,is

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