## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 9 Quadratic Relations and Conic Sections - 9.6 Translate and Classify Conic Sections - 9.6 Exercises - Skill Practice - Page 656: 33

parabola

#### Work Step by Step

All conics' equations are in the form $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$. In this the discriminant is $D=B^2-4AC$. Then we have $4$ cases: 1) $D\lt0,B=0,A=C$, then the conic is a circle 2) $D\lt0$ but $B\ne0$ or $A\ne C$, then it is an ellipse 3) $D=0$, then it is a parabola 4) $D\gt0$, then it is a hyperbola. Hence here $D=0^2-4(1)(0)=0$, thus it is a parabola.

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