Question

differential equations of sphere whose centre lie on z-axis
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Answer 1

Answer: Required equation is

x2+y2+(z−c)2=r2...(1)

Differentiating partially w.r. to x and y we get

2x+2(z−c)p=0

2y+2(z−c)q=0

⇒(z−c)p=−x...(2)

(z−c)q=−y...(3)

(2)(3)⇒pq=xy⇒xq=yp