The line 12xcosθ + 5ysinθ = 60 is tangent to which of the following...

Given that $12xcos\theta + 5ysin\theta = 60$

Divide the above equation with $60$ on both sides

$\dfrac{xcos\theta}{5} + \dfrac{ysin\theta}{12} = 1 \ldots \left(i\right)$

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

$⇒$ Equation of tangent at point $( acos\theta, bsin\theta )$
$\dfrac{xacos\theta}{{a}^{2}} + \dfrac{ybsin\theta}{{b}^{2}} = 1$

$\dfrac{xcos\theta}{a} + \dfrac{ysin\theta}{b} = 1 \ldots$\left(ii\right)$</p><p>Using equation \left(i\right)$ and \left(ii\right)$⇒ a = 5$
$b = 12$
Equation of ellipse is $\dfrac{{x}^{2}}{25} + \dfrac{{y}^{2}}{144} = 1$