Question

If afb is a focal chord oof parabola y²=4ax and af=4 , fb=5 , then the latus rectum of the parabola is equal to

Answer 1

Answer:

The latus rectum of the parabola $y^{2} = 4ax$ is equal to $\frac{80}{9}$ with a focal cord afb whose af = 4 and fb = 5

Step-by-step explanation:

As we know that the latus rectum for the parabola $y^{2} = 4ax$ with a focal cord afb is equal to 4a.

To find the value of a, we have

$\frac{1}{a} =\frac{1}{af}+\frac{1}{fb}$

So, by putting values of af and fb we get

$\frac{1}{a} =\frac{1}{4}+\frac{1}{5} = \frac{5+4}{20} = \frac{9}{20}$

We get $a = \frac{20}{9}$

For latus rectum, we get

$4a = 4(\frac{20}{9} ) = \frac{80}{9}$

Hence, latus rectum = $\frac{80}{9}$

I hope this answer may help you