# Chapter 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 8

True

#### Work Step by Step

The general equation of a conic has the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0(1)$ (a) When $B^2-4AC=0$, then a conic defines a parabola. (b) When $B^2-4AC \lt 0$, then a conic defines an ellipse and $A\ne C$ (c) When $B^2-4AC \lt 0$, then a conic defines a circle and $A=C$ (d) When $B^2-4AC \gt 0$, then a conic defines a hyperbola. We have: $A=a,B=0,C=6$. Plug these values in Equation (1) to obtain: $B^2-4AC=(0)^2-4(a)(6)=-24a$ The conic will represent an ellipse when $-24a \lt 0 \\ -a \lt 0 \\ a \gt 0$ Therefore, the statement is True.

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