Question

Please give appropriate answer.


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

Answer 1

Let $A(3,6),B(-3,4),P(x,y)$.

Then,

$\overline{PA}^{2}=\overline{PB}^{2}$

$\hookrightarrow (x-3)^{2}+(y-6)^{2}=(x+3)^{2}+(y-4)^{2}$

$\hookrightarrow -6x+9-12y+36=6x+9-8y+16$

$\hookrightarrow 12x+4y-20=0$

$\hookrightarrow 3x+y-5=0$

The red line is the equation of a line satisfying the relation of $\overline{AP}=\overline{BP}$, hence the relation is satisfied.