Question

a) which is equation of the parabola? b) name the focus and directrix ? c) name vertex and axis of symmetry?

Answer 1

The equation of the parabola whose axis of symmetry is parallel to x-axis is

$(y-k)^2=4p(x-h)$

where the focus is

$\text{focus}=(h+p,k)$

and the directrix is

$x=h-p$

In our case, the focus is (6,1) and the directrix is x =2; therefore, we have

$(6,1)=(h+p,k)$

and

$h-p=2$

These equations give

$k=1,h=4,p=2$

Hence, the equation of the parabola is

$(y-1)^2=8(x-4)$