Question

Find the equation of the ellipse whose foci are at(0,-5) and (0,5) and the length of its major axis is 14

Answer 1

Solution:

Given, foci are (0, -5) and (0, 5).

Here, $c=5$

Also, length of major axis is 14.

So, $2a=14$

or, $a=7$

So, this ellipse lies along y-axis, i.e. major axis is y-axis.

Also, (0, 0) is the centre of the ellipse.

Consider its equation: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ ...(i)

We know that, $b^2=a^2-c^2$

$\Rightarrow b^2=7^2-5^2$ [Putting values]

$\Rightarrow b^2=49-25=24$

Putting values of a and $b^2$ in (i), we get

$\dfrac{x^2}{7^2}+\dfrac{y^2}{24}=1$

$\Rightarrow \dfrac{x^2}{49}+\dfrac{y^2}{24}=1$

Answer: $\dfrac{x^2}{49}+\dfrac{y^2}{24}=1$