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

JEE Main 2022 Mathematics question

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

Answer: 9

Solution

The parabola is = −x/2. The tangent of slope m is y = mx − 1/(8m). Through (2, 0): 2m = 1/(8m), so and . The tangents are 4y = x − 2 and 4y = −x + 2, i.e. x −

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Question ID VK-034710