Question: How would I go about solving the following question?

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> Find the equations of the lines that are tangent to the ellipse $x^2 + 4y^2 = 16$ and that also pass through the point $(4,6)$
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Please provide some hints/clues

Thanks!

Answer: 
Given a point $(a,\frac 14 \sqrt{16-a^2})$ on the ellipse, you can take the derivative to find the slope of the tangent. You can then use the [point-slope form](http://en.wikipedia.org/wiki/Point-slope_formula#Point.E2.80.93slope_form) for the line and see if it goes through $(4,6)$ If you do this generally, you will get an equation in $a$ that you can solve.
Equation of tangent to ellipse $$x^2/a^2+y^2/b^2=1$$ at point $T(x\_0,y\_0)$ is 
$$xx\_0/a^2+yy\_0/b^2=1$$