Question

If one end point of the focal chord of the parabola $y^2=4ax$ is $(1,2)$, then second end point lies on

• A. $x^{2}y+2=0$
• B. $xy+2=0$
• C. $xy-2=0$
• D. $x^2+xy-y-1=0$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $x^{2}y+2=0$
B $xy+2=0$
D $x^2+xy-y-1=0$

For $y^2=4x$
$a=1$ then $(1,2)\equiv (t_1^2,2t_1)$
By comparing, we get,
$t_1=1$
for second end point $(t_2^2,2t_2)$
and
$t_1{t}_1=-1\Rightarrow t_2=-1$
So, second end point will be $(1,-2)$
Now checking options
$1^2\times (-2)+2=0$ , satisfied
$1\times (-2)+2=0$ , satisfied
$1\times (-2)-2=-4\ne 0$ , Not satisfied
$1^2+1\times (-2)-(-2)-1=0$ , satisfied