Question

Find the equation of the locus of point such that the sun of the squares of its distances from A(3,0) and
B(-3,0) is four times the distance from A and B.

Answer 1

Answer:-

Let the point P be (x,y)

According to question,

x 2 +(y−2) 2 + x 2 +(y+2) 2 =6

⇒ x 2 +(y−2) 2−6= x 2 +(y+2) 2

On squaring both sides,

⇒x 2 +(y−2) 2 +36−12 x 2 +(y−2) 2

=x 2 +(y+2) 2

⇒36+y 2 +4−4y=12 x 2 +(y−2) 2 +y 2 +4+4y

⇒36−4y=12 x 2 +(y−2) 2 +4y

⇒36−8y=12 x 2 +(y−2) 2

⇒9−2y=3 x 2 +(y−2) 2

Again on squaring both sides,

⇒81+4y 2 −8y=9x 2 +9y 2 +36−36y

⇒9x 2 +5y 2 −28y−45=0, which is the required locus.

Hope it helps