Question

$(\frac{1}{2},2)$ is one extremity of a focal chord of the parabola $y^2=8x$. The coordinates of the other extremity is

• A. (8, 8)
• B. (–8, 8)
• C. (8, –8)
• D. (–8, –8)

Answer 1

The correct option is C (8, –8)

For the parabola $y^2=8x$; focus S(2, 0). Given point is $P(\frac{1}{2},2)$
$Slopeof\overleftrightarrow{SP}is\frac{2-0}{\frac{1}{2}-2}=-\frac{4}{3}$
Equation to $\overleftrightarrow{SP}is4x+3y-8=0$
$4x+3y-8=0\Rightarrow 4x=8-3y$
Substituting this value of 4x in $y^2=8x$ we get $y^2=2(8-3y)\Rightarrow y^2+6y-16-16=0\Rightarrow (y+8)(y-2)=0$
$\Rightarrow y=2or-8$
$y=-8\Rightarrow 4x=8-3(-8)=32\Rightarrow x=8$ $\therefore$ point is (8, –8).