MCQ
If $x = a \cos \theta$ and $y = b \sin \theta$, then $b ^2 x ^2+ a ^2 y ^2=$
- ✓$a^2 b^2$
- B$ab$
- C$a^4 b^4$
- D$a^2+b^2$
✓
Answer
Correct option: A.
$a^2 b^2$
$\text{x}=\text{a}\cos\theta,\text{y}=\text{b}\sin\theta\ .....(\text{i})$
$\text{bx}=\text{ab}\cos\theta,\text{ay}=\text{ab}\sin\theta\ .....(\text{ii})$
Adding $(i)$ and $(ii)$ we get,
$=\text{b}^2\text{x}^2+\text{a}^2\text{b}^2\cos^2\theta+\text{a}^2\text{b}^2\sin^2\theta$
$=\text{a}^2\text{b}^2(\cos^2\theta+\sin^2\theta)$
$=\text{a}^2\text{b}^2\times1$
$=\text{a}^2\text{b}^2$
$\text{bx}=\text{ab}\cos\theta,\text{ay}=\text{ab}\sin\theta\ .....(\text{ii})$
Adding $(i)$ and $(ii)$ we get,
$=\text{b}^2\text{x}^2+\text{a}^2\text{b}^2\cos^2\theta+\text{a}^2\text{b}^2\sin^2\theta$
$=\text{a}^2\text{b}^2(\cos^2\theta+\sin^2\theta)$
$=\text{a}^2\text{b}^2\times1$
$=\text{a}^2\text{b}^2$
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