Question

If PQ is a focal chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ Which passes through S=(3,0) and PS=2 then length of the chord PQ is equal to

• A. 10
• B. 5
• C. 4
• D. 2

Answer 1

The correct option is A 10

We have,

Equation of ellipse is $\frac{x^2}{25}+\frac{y^2}{16}=1......\left(1\right)$

Now we can write this,

$\frac{x^2}{5^2}+\frac{y^2}{4^2}=1$

On comparing this ,

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

Then,

$a=5,b=4$

Now,

Using formula,

$b^2=a^2(1-e^2)$

$\Rightarrow 16=25(1-e^2)$

$e=\frac{3}{5}$

So, focus

$S=(ae,0)=(3,0)$

Now,

$PS=2Also,AS=2$

$PS=AS$

Then, It will be Circle.

$PQ=A{A}^{\prime }=2a=2\times 5=10$

Hence, the chord of length is $10$

Hence, this is the answer.