Two tangent lines l1 and l2 are drawn from the point (2,0) to the parabola 2 y2=-x. If the lines l1 and l2 are also tangent to the circle (x-5)2+y2=r, then 17 r is equal to

Question

Two tangent lines l1 and l2 are drawn from the point (2,0) to the parabola 2 y2=-x. If the lines l1 and l2 are also tangent to the circle (x-5)2+y2=r, then 17 r is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

y2=-(x/2) y=m x-(1/8 m) this tangent pass through (2,0) m =± (1/4) i.e., one tangent is x-4 y-2=0 17 r =9

Q. Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point $(2, 0)$ to the parabola $2 y^{2} = - x$ . If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x - 5)^{2} + y^{2} = r$ , then $17 r$ is equal to

$y^{2} = - \frac{x}{2}$
$y = m x - \frac{1}{8 m}$
this tangent pass through $(2, 0)$
$m = \pm \frac{1}{4}$
i.e., one tangent is $x - 4 y - 2 = 0$
$17 r = 9$

Q. Two tangent lines l1​ and l2​ are drawn from the point (2,0) to the parabola 2y2=−x. If the lines l1​ and l2​ are also tangent to the circle (x−5)2+y2=r, then 17r is equal to

y2=−2x​ y=mx−8m1​ this tangent pass through (2,0) m=±41​ i.e., one tangent is x−4y−2=0 17r=9

Q. Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point $(2, 0)$ to the parabola $2 y^{2} = - x$ . If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x - 5)^{2} + y^{2} = r$ , then $17 r$ is equal to

$y^{2} = - \frac{x}{2}$
$y = m x - \frac{1}{8 m}$
this tangent pass through $(2, 0)$
$m = \pm \frac{1}{4}$
i.e., one tangent is $x - 4 y - 2 = 0$
$17 r = 9$