Answer to Question #308159 in Differential Equations for vyom

Question #308159

form a partial differential equation for (x− a)² + (y−b)² + z² = 1


1
Expert's answer
2022-03-13T17:48:02-0400

(x - a)2 + (y – b)2 + z2 = c2   ........(1)

Differentiating (1) w.r.t ‘x’

2(x−a)+0+2zdz/dx=0

2(x-a) =-2zdz/dx

(x-a)=- zdz/dx .......(2)

Differentiating (1) with respect to y

0+2(y-b)+2zdz/dy =0

2(y-b)=-2zdz/dy

(y-b) = -zdz/dy.....(3)

Inserting 2 and 3 in the equation 1

We have, (-zdz/dx)2 + (-zdz/dy)2 +z2=c2

Let dz/dx be p and dz/dy be q

We have,

(-zp)2+(-zq)2+z2 =c2

z2 (p2 + q2 + 1) = c2

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS