Question

The locus of a point whose chord of contact with respect to parabola
$y^2=8x$ passes through focus is

• A. $x+2=0$
• B. Directrix of the given parabola
• C. $x+1=0$
• D. Latus ractum of the given parabola

Answer 1

Answer: (A), (B)

Directrix of the given parabola

Let the point be $P(h,k)$

Equation to the chord of contact drawn from point $P(h,k)isT=0$

$ky=4(x+h)$ - - - - - - (1)
This equation passes through the focus $(a,0)\equiv (2,0)$ substituting $x=2\&y=0$ in equation (1)

$k\times 0=4(2+h)$

$4(2+h)=0$

$2+h=0$

For locus of the point replace h by $x$

$x+2=0$

This is also an equation of directrix of the parabola
$y^2=8x.$