tangent line, implicit differentiation

**Tweety** · May 19th 2010, 09:10 PM

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

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

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

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

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

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

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

thank you.

**Random Variable** · May 19th 2010, 09:50 PM

then $-\frac{x}{4y} = - \frac{3}{2}$

or $x = 6y$

so $(6y)^{2} + 4 y^{2} = 4$

or $y = \pm \frac{1}{\sqrt{10}}$

now just plug back in the y-values to find the x-values

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