Question

A variable plane is at a constant distance $2p$ from the origin and meets the coordinate axes in point $A$, $B$ and $C$ respectively. Through these points, planes are drawn parallel to the coordinates plane. Find the locus of their point of intersection

• A. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{4p^2}$
• B. $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$
• C. $\frac{16}{x^2}+\frac{16}{y^2}+\frac{16}{z^2}=\frac{1}{p^2}$
• D. $xyz=p^3$

Answer 1

Answer: (A)

Lets Consider normal to plane be $a\hat{i}+b\hat{j}+c\hat{k}$
Plane equation of unit normal vector $\hat{n}$ and perpendicular distance between origin and plane is $d$ then plane equation is $\hat{n}.(x\hat{i}+y\hat{j}+z\hat{k})=d$