Find equation of quadratic when given tangents? I know the equations of 4 lines which are tangents to a quadratic:
$y=2x-10$
$y=x-4$
$y=-x-4$
$y=-2x-10$
If I know that all of these equations are tangents, how do I find the equation of the quadratic?
Normally I would be told where the tangents touch the curve, but that info isn't given.
Thanks!

As they are symmetric around the origin, the quadratic has no linear term in $x$.  So I would put $y^2=ax^2+b$ as any linear term in $y$ can be absorbed into a vertical shift or $y=ax^2+b$ to get the parabolas.  Then calculate what $a$ and $b$ need to be to make them tangent.  Because we incorporated the symmetry, you only have two tangent lines, but that gives two equations for $a, b$.
