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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^2 is equal to

Correct answer

0

Step-by-step solution

Given, from point 2 , 0 tangents are drawn on 2 y 2 = - x , these tangents also touches the circle x - 5 2 + y 2 = r 2 , then value of 17 r 2 is: Now equation of tangents when point is outside will be y = m x - 1 8 m , now 2 , 0 will lie here so m = ± 1 4 , putting the value of m we get, x - 4 y = 2 and 4 y + x = 2 Using distance of centre from tangent equal to radius, we get 5 - 0 - 2 17 = r or 5 + 0 - 2 17 = r ∴     r 2 = 9 17 ⇒   17 r 2 = 9

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