Question

kindly answer correctly I gonna make brainlist for sure if wrong I goona report u for sure​

Answer 1

Answer:

Option 1) is correct. Latus rectum is

$\frac{2a}{4} = \frac{a}{2} .$

Step-by-step explanation:

For a given hyperbola, say

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1$

its eccentricity is given by,

$e = \frac{c}{a}$

and the latus rectum is given by

$\frac{2 {b}^{2} }{a}$

and also

$b = \sqrt{{c}^{2} - {a}^{2} }$

Here,

$e = \frac{ \sqrt{5} }{2}$

, so we have

$c = \frac{ \sqrt{5} }{2} \times a$

and

$b = \sqrt{ \frac{5}{4} {a}^{2} - {a}^{2} } = \frac{a}{2} .$

So, latus rectum will be

$\frac{2 \times {b}^{2} }{a} = \frac{2 {a}^{2}}{4a} = \frac{a}{2} .$

Thus, length of latus rectum is 1.

Answer 2

Answer:

kindly refer to the attachments

hope it helps you