Question

Find the values of x, y if the distances of the point (x, y) from (−3, 0) as well as from (3,0) are 4.

Answer 1

We have P(x, y),Q(−3, 0) and R(3,0)

Squaring both sides

⇒ 16=x²+9+6x+y²

⇒ x²+y²=16-9-6x

⇒ x²+y²=7-6x   ..............(1)

Squaring both sides

⇒ 16=x²+9-6x+y²

⇒ x²+y²=16-9+6x

⇒ x²+y²=7+6x      ...........(2)

Equating (1) and (2)

⇒ 7-6x=7+6x

⇒ 7-7=6x+6x

⇒ 0=12x

⇒ x=0

Substituting the value of x=0 in (2)

⇒ x²+y²=7+6x

⇒ 0+y²=7+6x0

⇒ y²=7

⇒ y=±√7