Question

Let PSQ be the focal chord of the parabola $y^2=8x.$ if the length of SP = 6 then, SQ is equal to

• A. $3$
• B. $4$
• C. $6$
• D. none

Answer 1

The correct option is A $3$

Let PSQ be a focal chord of a parabola $y^2=8x$

Length of $SP=6cm$ $SQ=?$

Let

$P\equiv (a{t}^2,2at)=({2t}^2,4t)SP=6\sqrt{{({2t}^2-2)}^2+{(4t-0)}^2}=6{4t}^4+4-8t^2+16t^2=36t^4+2t^2-8=0t^2=\frac{-2\pm \sqrt{4+32}}{2}=-1\pm 3$

Where $-4$ is not accepted

$t^2=2t=\pm \sqrt{2}$

PQS is focal chord

$Q\equiv (\frac{a}{t^2},\frac{-2a}{t})=(1,\pm 2\sqrt{2})SQ=\sqrt{(2-1{)}^2+(0\mp 2\sqrt{2}{)}^2}=\sqrt{1+8}$

$=3$ Units