Question

Find a point on x-axis which is equidistant from (2, -5) and (-2, 9)

Answer 1

Let the required point on the x-axis be $(x,0).$

Therefore,

$\sqrt{(x-2{)}^2+(5{)}^2}=\sqrt{(x+2{)}^2+(-9{)}^2}$

$(x-2{)}^2+25=(x+2{)}^2+81$

$x^2+4-4x+25=x^2+4+4x+81$

$8x=25-81=-56$

$x=-7$

hence, the required point is $(-7,0)$.