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← JEE Main 2022 · 28 Jul · Shift 2
MathematicsInteger+4 / -1Question 85 of 90

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 85

Two tangent lines l1l_1 and l2l_2 are drawn from the point (2, 0) to the parabola 2y2=−x2y^2=-x. If the lines l1l_1 and l2l_2 are also tangent to the circle (x−5)2+y2=r(x-5)^2+y^2=r, then 17r is equal to ______.

Answer and worked solution

Official answer: 9

Tangents to y2=−x2y^2=-\frac x2 through (2, 0): m=±14m=\pm\frac14, e.g. x−4y−2=0x-4y-2=0.

Circle. The distance from (5, 0) is 317\frac3{\sqrt{17}}, so r=917r=\frac9{17}.

Answer: 9