A variable plane passes through a fixed point `(a ,b ,c)` and cuts the coordinate axes at points `A ,B ,a n dCdot` Show that eh locus of the centre of the sphere `O A B Ci s a/x+b/y+c/z=2.`

Explanation

To solve the problem, we need to show that the locus of the center of the sphere \( OABC \) is given by the equation:

\[ \frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 2 \]

where \( O \) is the origin, and \( A, B, C \) are the points where the variable plane intersects the coordinate axes.

...