Question

Find the points on y-axis, which are at a distance of 13 units each from the point (−5, 7).

Answer 1

Let the point on y-axis be B(0, b) and the given point be A(−5, 7).The distance between A and B is 13 units.
Now,
$$\begin{gathered} AB=13 \\ \Rightarrow \sqrt{{\left(0+5\right)}^2+{\left(b-7\right)}^2}=13 \\ \Rightarrow 25+b^2+49-14b=169 \\ \Rightarrow b^2-14b-95=0 \\ \Rightarrow \left(b-19\right)\left(b+5\right)=0 \\ \Rightarrow b=19\mathrm{or}-5 \end{gathered}$$
Hence, the points are (0, 19) and (0, −5).