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**imforumer** Given the equation of the ellipse $\displaystyle x^2+12y^2=48$

Find the equations of the tangents drawn from the point (4,6) and thier points of contact with the ellipse.

I got the gradient of the tangent which is $\displaystyle \frac{\,dy}{\,dx}=-\frac{x}{12y}$

Then I equate it with the gradient of the line

$\displaystyle -\frac{x}{12y}=\frac{y-6}{x-4}$

$\displaystyle -x(x-4)=12y(y-6)$

$\displaystyle 12y^2+x^2=72y+4x$

$\displaystyle 72y+4x=48$ Here is when Im stuck