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

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

(a) $a^{2} b^{2}$

(b) $a b$

(c) $a^{4} b^{4}$

(d) $a^{2}+b^{2}$

Solution:

Given:

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

So,

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

$=b^{2}(a \cos \theta)^{2}+a^{2}(b \sin \theta)^{2}$

$=b^{2} a^{2} \cos ^{2} \theta+a^{2} b^{2} \sin ^{2} \theta$

 

$=b^{2} a^{2}\left(\cos ^{2} \theta+\sin ^{2} \theta\right)$

We know that,

$\sin ^{2} \theta+\cos ^{2} \theta=1$

Therefore, $b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2}$

Hence, the correct option is (a).

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