Find the equation of the parabola on a picture if $|FL|=8$ units and $\angle KFO=60^o$. $F$ is given as the focus of the parabola.
We know that this parabola passes through the point $(0,0)$, so if I can find a different point lying on this parabola I can find its equation. But I can't find this point.
How can I solve this problem?
Guide: The equation of this parabola is $y^2=2px$ for some real (and negative) $p$. Then $F=({p\over 2},0)$ and a line $d$ has an equation $$y=\sqrt{3}\left(x-{p\over 2}\right)$$
Solving the equation $$3\left(x-{p\over 2}\right)^2 = 2px$$you will get $x$ for $L$ (and $K$) and then you can calculate the $y$ for $L$. Use the fact $LF =8$ and the formula for the distance between two points and you will get a $p$.