Question

Find the square of the length of the chord cut from the line $x+y=8$ by the parabola $x^2=4y$.

Answer 1

Parabola: $x^2=4y.......\left(i\right)$

Line: $x+y=8..........\left(ii\right)$

Point of intersection of $\left(i\right)$ and $\left(ii\right)$ $=>y=16,4$

$x=-8,4$

So, $P(16,-8)$ and $Q(4,4)$

$P{Q}^2={(16-4)}^2+(-8-{4)}^2$

$={\left(12\right)}^2+(12{)}^2$

$=2\left(144\right)$

$=288.$