Question

A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3.

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

The vertex of parabola is origin and directrix of the parabola is y = 3.

The standard form of a parabola is

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

Where (h,k) is vertex. (h,k+p) is focus and y=k-p is directix.

The vertex of parabola is origin. So,

$h=0$

$k=0$

Directrix of the parabola is y = 3.

$y=k-p$

$3=0-p$

$-3=p$

The value of p is -3.

Focus of the parabola is (h,k+p).

$(h,k+p)=(0,0-3)$

$(h,k+p)=(0,-3)$

Therefore focus of the parabola is (0,-3) and option 3 is correct.

Answer 2

The coordinates of the focus are (3,0)