If one end of a focal chord of the parabola y^2=16x is at (1,4), then the length of this f…

Question

If one end of a focal chord of the parabola $y^2=16x$ is at $(1,4)$, then the length of this focal chord is:

Accepted Answer

$a=4$; using $(at^2,2at)$: $2(4)t=4\Rightarrow t=\dfrac12$.

$$\text{Focal chord length}=a\left(t+\frac1t\right)^2=4\left(\frac12+2\right)^2=4\left(\frac52\right)^2=25.$$

Solutions · 1