Question

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

$x^2+xy-y-1=0$

$(1,2)$ satisfy the given parabola $y^2=4ax$
$\therefore a=1$
Now,
$(1,2)\equiv (t_1^2,2t_1)\Rightarrow t_1=1$

Other end point of the focal chord is $(t_2^2,2t_2)$
Where
$t_1{t}_2=-1\Rightarrow t_2=-1$
So, other end point is $(1,-2)$

Now checking the options
$x^{2}y+2=0,xy+2=0$ and $x^2+xy-y-1=0$ passes through $(1,-2)$