Question

If the sum and difference of the ordinates of the end point of a chord of the parabola $y^2=4x$ is $\sqrt{20}$ and $2$ respectively, then the length of chord is units

Answer 1

Let $A(a{t}_1^2,2a{t}_1)$ and $B(a{t}_2^2,2a{t}_2)$ is the end points of chord
Where $a=1$
Given : $2a{t}_1+2a{t}_2=\sqrt{20}$
$\Rightarrow t_1+t_2=\sqrt{5}\cdots \left(i\right)$
Also,
$|2a{t}_1-2a{t}_2|=2\Rightarrow |t_1-t_2|=1\cdots \left(ii\right)$

Now, the length of chord
$=|a(t_1-t_2)|\sqrt{(t_1+t_2{)}^2+4}$
Using equation $\left(1\right)$ and $\left(2\right)$, we get
$=3$