Question

If $x=a\cos \theta \text{and}y=b\sin \theta$, then $b^2{x}^2+a^2{y}^2$ is equal to

• A. $ab$
• B. $a^2{b}^2$
• C. $a^4{b}^4$
• D. none of these

Answer 1

The correct option is B $a^2{b}^2$

$x=a\cos \theta ;y=b\sin \theta$

$\cos \theta =\frac{x}{a};\sin \theta =\frac{y}{b}$

${\cos }^2\theta +{\sin }^2\theta =1=\frac{x^2}{a^2}+\frac{y^2}{b^2}$

$x^2{b}^2+a^2{y}^2=a^2{b}^2$.