Question

Someone help me do this question am giving brainliest

Answer 1

Step-by-step explanation:

Given:

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

or

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

Let $x = r\cos{\theta}$ and $y = \sin{\theta}.$ Substituting these into our given equation, we get

$b^2x^2 + a^2y^2 = a^2b^2$

Dividing both sides by $a^2b^2,$ we get

$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$

which we recognize as an equation for an ellipse.