Question

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axis is $\frac{1}{2}$. The plane passes through the point ____________.

Answer 1

For a variable plane, given sum of reciprocal of its intercept is $\frac{1}{2}$ let a,b,c be the intercepts with co-ordinates axes according to given condition,
$$\begin{gathered} \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{2} \\ \mathrm{i}.\mathrm{e}.\frac{2}{a}+\frac{2}{b}+\frac{2}{c}=1 \\ \mathrm{i}.\mathrm{e}.2\left(\frac{1}{a}\right)+2\left(\frac{1}{b}\right)+2\left(\frac{1}{c}\right)=1 \end{gathered}$$
i.e plane passes through fixed point (2, 2, 2,)