Question

$PS{P}^1$ is focal chord of the ellipse $4x^2+9y^2=36$. If SP$=4$ then $S{P}^1$ is

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{4}{3}$
• D. $\frac{4}{5}$

Answer 1

The correct option is D $\frac{4}{5}$

Equation of ellipse,

$\frac{x^2}{9}+\frac{y^2}{4}=1$

$a=3,b=2$.

As we know that,

semi latus rectum is the Harmonic mean of segments $PS$ and $S{P}^1$ of focal chord,

Mathematically,

$\frac{b^2}{a}=\frac{2\left(SP\right)\left(S{P}^{\prime }\right)}{SP+S{P}^1}$

$\frac{2^2}{3}=\frac{2\left(4\right)\left(S{P}^{\prime }\right)}{4+S{P}^1}$

$16+4S{P}^1=24S{P}^1$

$S{P}^1=\frac{4}{5}$