If the common tangents to the parabola, x^2 = 4y and the circle, x^2+y^2 = 4 intersect at the point P, then the distance of P from the origin (units), is:

JEE Main 2017 Mathematics question

If the common tangents to the parabola, and the circle, intersect at the point , then the distance of from the origin (units), is:

Answer: (4)

Write a tangent to in slope form. Substituting gives , and tangency requires a repeated root: , i.e. . So every tangent is

y = mx - .

For this line to touch the circle of radius centred at the origin, the perpendicular distance

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Question ID VK-115832