Question

PSQ is a focal chord of the parabola $y^2=8x$ .If $SP=6$ then $\frac{SP}{SQ}=$

• A. $\frac{3}{4}$
• B. $\frac{2}{3}$
• C. $\frac{1}{9}$
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

$\frac{2}{3}$

The co-ordinate of a local chord of a parabola are $P({at}^2,2at)$ and $Q(\frac{a}{t^2},\frac{-2a}{t})$

$y^2=8x$

comparing with $y^2=4ax$ we get $a=2$

Hence co-ordinates of focus is $(2,0)$.

$sp=6{sp}^2=36{(2-{2t}^2)}^2+{\left(4t\right)}^2=36$

solving it we get,

$t^4+2t^2-8=0t^2=2\therefore SQ=3\frac{SP}{SQ}=\frac{2}{3}$