Chapter 10 - Analytic Geometry - 10.4 Summary of the Conic Sections - 10.4 Exercises - Page 996: 36

$${\text{ellipse}}$$

$$\eqalign{ & 9{x^2} + 36{y^2} = 36 \cr & {\text{Divide by 36}} \cr & \frac{{9{x^2}}}{{36}} + \frac{{36{y^2}}}{{36}} = \frac{{36}}{{36}} \cr & \frac{{{x^2}}}{4} + {y^2} = 1 \cr & {\text{The equation is in the form }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr & {\text{Therefore, the equation represents an ellipse}} \cr & {\text{Graph}} \cr} $$