Question

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

$\frac{x}{a}sin\theta$ - $\frac{y}{b}cos\theta$ = 1

Answer 1

$\frac{x^2}{a^2}co{s}^2\theta$ + $\frac{y^2}{b^2}si{n}^2\theta$ + $\frac{2xy}{ab}sin\theta cos\theta$ = 1

$\frac{x^2}{a^2}si{n}^2\theta$ + $\frac{y^2}{b^2}co{s}^2\theta$ - $\frac{2xy}{ab}sin\theta cos\theta$ = 1

(+) (+) (-) (+)

$\frac{x^2}{a^2}$ + $\frac{y^2}{b^2}$ = 2 [$\because si{n}^2\theta co{s}^2\theta =1$]