## find the locus of the point p such that PA2+pb2=2c2 where A(a,0),B(-a,o) and 0<|a|<|c|​

Question

find the locus of the point p such that PA2+pb2=2c2 where A(a,0),B(-a,o) and 0<|a|<|c|​

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1 month 2021-08-19T02:33:18+00:00 2 Answers 0 views 0

1. Q):-Find the equation of locus of a point P such that PA^2+PB^2=2C^2,Where A (a,0), B (-a,0) and o <11<|c|.

x^2+y^2+a^2-c^2=0.

## Explanation:-

Let P (x,y) be a point on the locus

given A (a,0),B (-a,0)

given condition is PA^2+PB^2=2C^2

(x-a)^2+(y-0)^2+(x+a)^2+(y-0)^2=2C^2

x^2+a^2-2ax+y^2+x^2+a^2+2ax+y^2=2C^2

2x^2+2y^2+2a^2-2C^2=0

2 (x^2+y^2+a^2-c^2)=0

x^2+y^2+a^2-C^2=0.

Therefore Equation of locus of P is x^2+y^2+a^2-C^2=0.

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