The major axis of an ellipse is y = x and one vertex is at origin, the other axis of the ellipse, if the length of semi-major axis be 10, can be

$$\begin{gathered} \mathrm{Given} \mathrm{that} \mathrm{a}=10 \\ slope of the line y=x is 1 \\ Now slope of another axis is \mathrm{m}=-1 \\ Now equation of another axis pas\sin g \mathrm{through} \left(\frac{10}{\sqrt{2}},\frac{10}{\sqrt{2}}\right) is \end{gathered}$$ 

$$\begin{gathered} \mathrm{y}-\frac{10}{\sqrt{2}}=-1\left(\mathrm{x}-\frac{10}{\sqrt{2}}\right) \\ \Rightarrow \mathrm{x}+\mathrm{y}=10\sqrt{2} \end{gathered}$$