Question

Find the equation of tangents to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ making an angle of ${60}^o$ with the major axis.

Answer 1

Equation of ellipse is
$\frac{x^2}{16}+\frac{y^2}{9}=\mathrm{1....}\left(i\right)$
Here, $a^2=16,b^2=9$
Slope of the tangent $\left(m\right)=\tan {60}^o=\sqrt{3}$.
$\therefore$ equation of tangents to $\left(i\right)$ making an angle of ${60}^o$ with the major axis are
$y=\sqrt{3}x\pm \sqrt{\left(16\right)\left(3\right)+9}$ $[y=mx\pm \sqrt{a^2{m}^2+b^2}]$
$y=\sqrt{3}x\pm \sqrt{57}$