Question

find the locus of a point whose sum of square of distances from two fixed points (a,0) and (-a,0) 2c² .​

Answer 1

Answer:

The equation of required locus is x² + y² = c² - a²

Step-by-step explanation:

Let P (x, y ) be any moving point.

Let A(a,0) and B( -a, 0)

Given :

PA² + PB² = 2c²

(x - a)² + (y - 0)² + (x + a )² +(y - 0)² = 2c²

x² + a² - 2ax + y² + x² + a² + 2ax + y² = 2c²

2x² + 2y² + 2a² - 2c² = 0

x² + y² + (a² - c²) = 0

x² + y² = c² - a²

This is the eqn of required locus.