Question

If x = a cos θ and y = b sin θ, then b²x² + a²y² =

Options

• a² b²

• ab

• a⁴ b⁴

• a² + b²

Answer 1

Given: 

`x= a cosθ, y= b sin θ` 

So,

`b^2 x^2+a^2 y^2` 

= `b^2(a cos)^2+a^2(b sin θ)^2` 

=` b^2 a^2 cos^2θ+a^2 b^2 sin^2θ`

=`b^2a^2 (cos^2 θ+sin^2θ)` 

We know that,

`sin^2θ+cos^2θ=1`

Therefore,` b^2x^2+a^2y^2=a^2b^2`