ParabolaHardBloom L3
Question
The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by:
Options
A.$24/5$
B.$12/5$
C.$6/5$
D.None of these
Solution
Sol. [Key Concept: For a focal chord, $\frac{1}{SP} + \frac{1}{SQ} = \frac{1}{a}$ (semi-latus rectum $= 2a$); solve with $SP = 3,\ SQ = 2$.]
$SP$, semi latus rectum, $SQ$ are in H.P.
$$\Rightarrow \frac{2}{2a} = \frac{1}{SP} + \frac{1}{SQ} = \frac{1}{3} + \frac{1}{2} = \frac{5}{6} \Rightarrow \ a = \frac{6}{5}\ \Rightarrow$$ Length of $LR = 4a = \frac{24}{5}$
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