Question

If the point $P(2,2)$ is equidistant from the points $A(-2,k)$ and $B(-2k,-3)$ , find $k$

Answer 1

$PA=PB\left(distance\right)$

$\sqrt{(2-(-2){)}^2+(2-K{)}^2}=\sqrt{[2-(-2K){]}^2+[2-(-3){]}^2}$

$16+(2-K{)}^2=(2+2K{)}^2+5^2$

$16+4-4K+K^2=4+4K^2+8K+25$

$\Rightarrow 0=3K^2+12K+9$

$\Rightarrow K^2+4K+3=0$

$(K+3)(K+1)=0$

$K=-1,-3$