Question

If $PSQ$ is a focal chord of the ellipse $16x^2+25y^2=400$ such that $SP=8$, then $SQ=$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

We have,
$16x^2+25y^2=400\Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1$
$\therefore$ Length of $L.R.=2\times \frac{16}{5}=\frac{32}{5}$
We know that the semi-latus rectum of an ellipse is the HM of the segments of a focal chord.
$\therefore$ HM of $SP$ and $SQ$ $=$ Semi-latusrectum
$\Rightarrow \frac{2SP.SQ}{SP+SQ}=\frac{16}{5}$
$\Rightarrow \frac{2\times 8\times SQ}{8+SQ}=\frac{16}{5}\Rightarrow 5Sq=8+SQ\Rightarrow SQ=2$