Question

x²/y+√x²+y²=-ay+b√x²+y² find a and b values​

Answer 1

Answer:

x=rcosθcosϕ;y=rcosθsinϕ;z=rsinθ

x

2

+y

2

+z

2

=r

2

.

x

2

=r

2

cos

2

θcos

2

ϕ

y

2

=r

2

cos

2

θsin

2

ϕ

z

2

=r

2

sin

2

θ.

r

2

cos

2

θcos

2

ϕ+r

2

cos

2

θsin

2

ϕ+r

2

sin

2

θ=r

2

r

2

(cos

2

θcos

2

ϕ+cos

2

θsin

2

ϕ+sin

2

θ)=r

2

r

2

[cos

2

θ(sin

2

ϕ+cos

2

ϕ)+sin

2

θ]=r

2

r

2

[cos

2

θ(1)+sin

2

θ]=r

2

r

2

(1)=r

2

∴r

2

=r

2

∴ Hence Proved x

2

+y

2

+z

2

=r

2