Question

The equation of chord to the parabola $y^2=4x$ whose sum of ordinates and product of abscissas of the endpoints of the chord is $4$ and $9$ respectively, is :

• A. $2x-2y+6=0$
• B. $2x-2y-6=0$
• C. $3x-2y+3=0$
• D. $3x-2y-3=0$

Answer 1

Answer: (A), (B)

$2x-2y-6=0$

Let the endpoints of the chord are $A(a{t}_1^2,2a{t}_1)$ and $B(a{t}_2^2,2a{t}_2)$
Where $a=1$, so
$A=(t_1^2,2t_1),B=(t_2^2,2t_2)$
Now,
$2t_1+2t_2=4\Rightarrow t_1+t_2=2\cdots \left(1\right)$
Also,
$t_1^2\times t_2^2=9\Rightarrow t_1{t}_2=\pm 3\cdots \left(2\right)$

Equation of the chord is given by
$2x-y(t_1+t_2)+2a{t}_1{t}_2=0$
From equation $\left(1\right)$ and $\left(2\right)$, we get
$2x-2y\pm 6=0$