Question

find the differential equations of all spheres of radius 10 and centres lying on plane x+y=0​

Answer 1

Explanation:

I need to form a pde of the set of all spheres whose centers lie on the x− axis.

For, (x−a)2+y2+z2=r2→(1), is an equation of the spheres whose center is at x axis and radius r.

Here a and r are arbitrary constants, I need to eliminate a and r to form a pde of (1).

If ∂z∂x=p,∂z∂y=q, we have (1) becomes z2(p2+q2+1)=r2.→(2)