Find the equation of the parabola whose vertex is the origin and whose directrix is x = -4

Try this option:

1) if V(0;0) and x= -4, then common view of the required equiation is:

(y-k)²=4p(x-h), where focus is in (h-p;k), the vertex is in (h;k), the directrix is x=h+p, p<0 and y=k is simmetry axis;

2) if the V(0;0), then h=k=0 and the required equiation is:

y²=4px;

3) if the directrix equation is x=h+p, where h=0, then p= -4 (according to the condition the directrix equation is x= -4), then the required equation is:

y²= -16x

y²= -16x

nope

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4