Question

Find the P. D. E of the family of sphere of radius 4 with centre on xy-plane​

Answer 1

Answer:

The equation for such spheres will be

(x − a)

2 + (y − b)

2 + u

2 = r

2

, (1)

where a, b are arbitrary and r is fixed.

Differentiating (1) with respect to x:

2(x − a) + 2uux = 0 ⇒ x − a = −uux.

Differentiating (1) with respect to y:

2(y − b) + 2uuy = 0 ⇒ y − b = −uuy.

Putting these back into (1):

u

2u

2

x + u

2u

2

y + u

2 = r

2

,

⇒ (u

2

x + u

2

y + 1)u

2 = r

2

.

Step-by-step explanation: