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

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

enter image description here

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

Narasimham
  • 40,495

1 Answers1

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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.

Emilio Novati
  • 62,675
  • I am asking for geometric interpretation of linear parameters $(h,k)$ and the dimensionless parameter $m$ but not how to derive it. – Narasimham Mar 27 '18 at 09:55
  • Since $A,B,C,D,E,F$ have a geometric meaning ( as you can see in the linked page), if you know how $h,k,m$ are derived you can find also their geometric interpretation. – Emilio Novati Mar 27 '18 at 12:19