0

Say we have a equation like $Ax²+Bxy+Cy²+2Dx+2Ey+F = 0$

What i thought was to first imply the condition that it does not represents a pair of straight line then if we consider the focus as $(a,b)$ and the directrix as $y=mx+c$ ,Now if we make the equation of parabola and then on simplifying we get that all the second degree terms form a perfect square.

But I think that observing the properties of a general equation of parabola and then implying it on the original second degree equation doesn't really helps to find all the sufficient conditions.

it would be really appreciated if someone provides all the sufficient condition required for the second degree equation to represent a parabola with derivation. Thank You

Anshu Gupta
  • 147
  • https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections and https://math.stackexchange.com/questions/1832616/discriminant-of-a-conic-section – Intelligenti pauca Oct 22 '23 at 11:32

0 Answers0