Find the equations of the tangents to the ellipse $\displaystyle x^{2} + 4y^{2} = 4 $

which are perpendicular t0 the line $\displaystyle 2x-3y = 1 $

I am not sure how to work out the equations of the tangents, when I have not been given a specified point,

$\displaystyle \frac{dy}{dx} = -\frac{x}{4y} $

$\displaystyle y = \frac{2}{3}x - \frac{1}{3} $

And if the tangents are perpendicular to the line, than it has to have a gradient of $\displaystyle -\frac{3}{2} $

that's all I am able to do, any help appreciated.

thank you.