Question

Write the equation of the ellipse with a minor axis length of 8 units and foci at (-7, 4) and (7, 4).

Answer 1

Given:

Minor axis length is 8 units.

Focci of elipse : (-7,4) and (7,4).

Required:

To find the equation of the elipse.

Explanation:

The general equation of elipse is

$\begin{gathered} \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ a>b \end{gathered}$

It is given that minor axis length is 8 units.

Therefore the value of b becomes 4.

Now we have to find the value of a.

And given that the focci points are (-7,4) and (7,4).

Here consider

$c=7$

Now,

$\begin{gathered} c^2=a^2-b^2 \\ 7^2=a^2-4^2 \\ 49=a^2-16 \\ 49+16=a^2 \\ a^2=65 \\ a=\sqrt{65} \end{gathered}$

Therefore, the equation of the elipse becomes

$\frac{x^2}{65}+\frac{(y-4)^2}{16}=1$

Final Answer:

$\frac{x^{2}}{65}+\frac{(y-4)^2}{16}=1$