﻿ Consider the family of circle x2 + y2 = r2, 2 < r < 5. If in the first quadrant the common tangent to a circle of the family and the ellipse 4x2 + 25y2 = 100 meets the coordinate axes at A and B, then find the equation of the locus of the mid point of AB. : Kaysons Education

# Consider The Family Of Circle x2 + y2 = r2, 2 < r < 5. If In The First Quadrant The Common Tangent To A Circle Of The Family And The Ellipse 4x2 + 25y2 = 100 Meets The Coordinate Axes At A and B, Then Find The Equation Of The Locus Of The Mid Point Of AB.

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## Question

### Solution

Correct option is

The equation of any tangent to the ellipse

It meets the coordinate of axes at

Let P(hk) be the mid-point of AB. Then

Since (i) touches the circle

Therefore,

Hence the locus of P(hk) is

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