How to prove that the given sphere is perpendicular

Asked May 02 '21 at 20:53

Active May 02 '21 at 21:02

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Given the sphere $x^2+y^2+z^2=ax, x^2+y^2+z^2=bx.$ How to prove that the given sphere is reciprocically normal.

My attemp is:

I find: $f_x(x,y,z)=2x-a,f_y(x,y,z)=2y,f_z(x,y,z)=2z$

$f_x(x,y,z)=2x-b,f_y(x,y,z)=2y,f_z(x,y,z)=2z$

but i dint know how to continue

edited May 02 '21 at 21:02

asked May 02 '21 at 20:53

hi hi

Why are they orthogonal? May be you wanted to say $by$ instead of $bx$ for the second sphere? – Math Lover May 02 '21 at 21:00
the first and the second sphere is reciprocically norma – hi hi May 02 '21 at 21:03
Please edit your question to define "reciprocally normal" since it isn't coming up in my first Google search. – RobertTheTutor May 02 '21 at 21:19

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