Question

Find a point on the Y - axis which is equidistant from the points A(-4,3) and B(6,5).

Answer 1

Let the point on y-axis be (0,y).

By, Distance formula we have,

$D=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Therefore,

$\sqrt{(4{)}^2+(y-3{)}^2}=\sqrt{(-6{)}^2+(y-5{)}^2}$

$16+y^2+9-6y=36+y^2+25-10y$

$25-6y=61-10y$

$4y=36$

$y=9$

Hence, the required point is $(0,9)$.