Question

The equation of the focal chord of the parabola $y^2=8x$ whose sum of ordinates of the endpoints of the chord is $8$, is

• A. $x+y+2=0$
• B. $x-y-2=0$
• C. $x-y+2=0$
• D. $x+y-2=0$

Answer 1

The correct option is B $x-y-2=0$

Let the endpoints of focal chord are $A(a{t}_1^2,2a{t}_1)$ and $B(a{t}_2^2,2a{t}_2)$
Where $a=2,t_1{t}_2=-1$
Now,
$2a{t}_1+2a{t}_2=8\Rightarrow t_1+t_2=2$

Equation of chord is
$2x-y(t_1+t_2)+2a{t}_1{t}_2=0$
Hence, the equation of the focal chord is
$2x-2y-4=0\Rightarrow x-y-2=0$