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

Question

The value of c, for which the line y = 2x + c is a tangent to the circle x 2 + y 2 =16 , is: (A)  - 16 √5  (B)  4 √5  (C)  16 √5  (D)  20

Tardigrade Admin · Accepted Answer

Given that, y = 2x + c ...(i) and x2 + y2 = 16 ...(ii) We know that y = mx + c is tangent to the circle x2 + y2 = a2, then c = ± a √ 1+m2 Here, m = 2 , a = 4 ∴ c = ± 4 √1+22 = ± 4 √ 5

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

$- 165$

$45$

$165$

$20$

Given that, $y = 2 x + c ... (i)$
and $x^{2} + y^{2} = 16 ... (ii)$
We know that $y = m x + c$ is tangent to the circle
$x^{2} + y^{2} = a^{2}$ , then
$c = \pm a 1 + m^{2}$
Here, $m = 2, a = 4$
$∴ c = \pm 4 1 + 2^{2}$
$= \pm 45$

Q. The value of c, for which the line y=2x+c is a tangent to the circle x2+y2=16 , is:

−165​

45​

165​

20