Find the equation of the tangent lines to the ellipse having a given angular coefficient Find the equations of the tangent lines to the ellipse $E : x^2/a^2 + y^2/b^2 − 1 = 0$ having a given angular coefficient $m ∈ R$.

Here's a go at it:
$$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$
Differentiate implicitly.
$$ \frac{2x}{a^2} + \frac{2y}{b^2}\frac{dy}{dx} = 0 $$
Assuming angular coefficient is the slope.
$$ \frac{dy}{dx} = m $$
$$ \frac{x}{a^2} + \frac{y}{b^2}m = 0 $$
$$ x  = - y \frac{a^2}{b^2}m $$
$$ x^2  = y^2 \frac{a^4}{b^4}m^2 $$
$$ y^2 \frac{a^2}{b^4}m^2 + \frac{y^2}{b^2} = 1 $$
$$ \frac{y^2}{b^2} \left[ \frac{a^2}{b^2}m^2 + 1 \right] = 1 $$
$$ y = \pm b \sqrt{ \frac{1}{ \left[ \frac{a^2}{b^2}m^2 + 1 \right] } } $$
You should be able to readily solve for the corresponding $x$ from here.
