Find a relation between x and y such that the point (x, y) is equ… - Vidyadip

Question

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).

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Answer

It is given that P (x,y) is equidistant from A(3, 6) and B(-3, 4).
Using Distance formula, we can write
$PA = PB$
$\sqrt {{{(x - 3)}^2} + {{(y - 6)}^2}} = \sqrt {{{[x - ( - 3)]}^2} + {{(y - 4)}^2}} $
$ \Rightarrow \sqrt {{x^2} + 9 - 6x + {y^2} + 36 - 12y} = \sqrt {{x^2} + 9 + 6x + {y^2} + 16 - 8y} $
Squaring both sides, we get
$\Rightarrow x^2+9-6 x+y^2+36-12 y=x^2+9+6 x+y^2+16-8 y$
$⇒ −6x − 12y + 45 = 6x - 8y + 25$
$⇒ 12x + 4y = 20$
$⇒ 3x + y = 5$

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