If the common tangents to the parabola, x 2 = 4y and the circle, x 2 + y 2 = 4 intersect at the poin

Q: JEE Main 2019 Conic Sections: If the common tangents to the parabola, x 2 = 4y and the circle, x 2 + y 2 = 4 intersect at the poin...

The correct answer is A. This problem asks us to find the distance from the origin to the intersection point of the common tangents to a given parabola and a circle. The key to solving this involves finding the general equations of tangents for both curves, identifying the common slopes, and then determining the intersection point of these common tangent lines. --- **1. Understanding the Problem and Key Concepts** Our goal is to find the coordinates of point P, where the common tangents intersect, and then calculate its

Question

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, is :

Accepted Answer

This problem asks us to find the distance from the origin to the intersection point of the common tangents to a given parabola and a circle. The key to solving this involves finding the general equations of tangents for both curves, identifying the common slopes, and then determining the intersection point of these common tangent lines.

1. Understanding the Problem and Key Concepts

Our goal is to find the coordinates of point P, where the common tangents intersect, and then calculate its distance from the origin $(0,0)$ .

The fundamental concepts we need are the standard forms of tangent equations for a parabola and a circle when the slope 'm' is known.

Tangent to a Parabola: For a parabola of the form $x^2 = 4ay$ , the equation of a tangent

Answer

Answer

2(3 + 2 )

Answer

2( + 1)

Answer

3 + 2

Question

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Solution

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