Thank you for reporting, we will resolve it shortly
Q.
Find the vertices and length of major axis of the ellipse $9x^{2} + 4y^{2 }= 36$.
Conic Sections
Solution:
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.