Question

The equation of the ellipse with vertices $(-4,3)$ and $(8,3)$ and $e=\frac{5}{6}$ is:

• A. $\frac{(x-2{)}^2}{36}+\frac{(y-3{)}^2}{11}=1$
• B. $\frac{x^2}{36}+\frac{y^2}{11}=1$
• C. $\frac{(x-2{)}^2}{11}+\frac{(y-1{)}^2}{36}=1$
• D. $\frac{(x-2{)}^2}{9}+\frac{(y-1{)}^2}{16}=1$

Answer 1

The correct option is A $\frac{(x-2{)}^2}{36}+\frac{(y-3{)}^2}{11}=1$

Given vertices of the ellipse as $(-4,3),(8,3)$
Center is the mid-point of the line segment joining the vertices.
So, coordinates of center is $(2,3)$
So, the equation of ellipse is of the form
$\frac{(x-2{)}^2}{a^2}+\frac{(y-3{)}^2}{b^2}=1$
The length of the major axis $=2a=12$
$\Rightarrow a=6$
Now, $b^2=a^2(1-e^2)$
$\Rightarrow b^2=36\left(\frac{11}{36}\right)$
$\Rightarrow b^2=11$
Hence, the equation of ellipse is
$\frac{(x-2{)}^2}{36}+\frac{(y-3{)}^2}{11}=1$