The Locus Of The Mid-point Of Te Portion Intercepted Between The Axes By The Line where p is Constant Is

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Question

The locus of the mid-point of te portion intercepted between the axes by the line where p is constant is

x² + y² = 4p²

medium

Solution

Correct option is

Let the line meet the x-axis and y-axis respectivelyA and B. then coordinates of A are and those of B are . If (h, k)is the mid-point of AB, then

To find the locus of (h, k) we have to eliminate . We have

And

Whence squaring and adding, we get

.

the required locus of (h, k) is

or

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