Geometric significace of oblique parabola parameters

Question

What is the geometric significance of constants $ (h,k,m) $ in this oblique parabola equation?

$$ y= m x \pm \sqrt{m x h + k^2}$$

Graph made with $ (h,k,m)=( 2,-1,0.5)$

Answer 1

Hint:

You can start from the general equation of a parabola: $$ Ax^2+Bxy+Cy^2+Dx+Ey+F=0 $$ with $B^2-4AC=0$, where the coefficients are linked to the properties of the parabola from classical results ( that you can see here).

Than solve the equation for $y$ and compare the result with your formula.