Question

Find the vertices and length of major axis of the ellipse $9x^2+4y^2=36$.

• A. $\left(0,\pm 3\right),6$
• B. $\left(0,\pm 3\right),4$
• C. $(3,0),-6$
• D. $\left(\pm 3,0\right),6$

Answer 1

Answer: (A)

The given equation of the ellipse can be written in standard form as $\frac{x^2}{4}+\frac{y^2}{9}=1$
Since the denominator of $\frac{y^2}{9}$ is larger than the denominator of $\frac{x^2}{4}$, the major axis is along the $y$-axis. Comparing the given equation with the standard equation $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$, we have $b=2$ and $a=3$.
Hence vertices are $(0,3)$ and $(0,-3)$ and length of the major axis is $6$ units.