Sarthaks Test
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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.

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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

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