In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at 0,5 3 , then the length of its latus rectum is:

Question

Aicharya · Accepted Answer

Given, difference of the lengths of major and minor axis is

10

.

\Rightarrow 2 b - 2 a = 10

… (1)
One of the focii is

(0, 5 \sqrt{3})

\Rightarrow b e = 5 \sqrt{3}

… (2)
Also

a^{2} = b^{2} (1 - e^{2})

.......(3)

\Rightarrow a^{2} = b^{2} - 75

\Rightarrow (b - a) (a + b) = 75

\Rightarrow a + b = 15

… (4)
From (1) and (4)

a = 5

and

b = 10

Hence length of the latus rectum

= \frac{2 a^{2}}{b} = 2 \cdot \frac{25}{10} = 5

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is…

Solution