I need help to solve for the equation of two tangent lines to the ellipse $x^2 -12x+y^2+7=0$, which pass through the origin. I've tried a variety of methods from searching similar problems on the internet, however, I can't seem to arrive at an answer.
I know from implicit differentiation that the derivative of $x^2 -12x+y^2+7=0$ with respect to $y$, is defined as:
$y' = \frac{(6-x)}{y}$
And, after that, I'm stumped. How do I go from there? Any help will be much appreciated.
Thank you in advance!