Question

If x = a cos θ and y = b sin θ, then (b²x² + a²y²) = ?
(a) a² + b²
(b) a²b²
(c) ab
(d) a⁴b⁴

Answer 1

(b) a²b²

$$\begin{gathered} x=a\text{cos}\theta \text{and}y=b\text{sin}\theta \\ \text{=>cos}\theta \text{=}\frac{x}{a}\text{and sin}\theta \text{=}\frac{y}{b} \\ {\text{We know that cos}}^2\theta +{\text{sin}}^2\theta =1 \\ \text{=>}{\left(\frac{x}{a}\right)}^2+{\left(\frac{y}{b}\right)}^2=1 \\ \text{=>}\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ \text{=>}\frac{x^2{b}^2+y^2{a}^2}{a^2{b}^2}=1 \\ \text{=>}{b}^2{x}^2+a^2{y}^2=a^2{b}^2 \end{gathered}$$