Using given coordinate of the focus and the equation of the directrix, Equation of a parabola is
(y-3)²=4(3)(x-(-1))
(y-3)²=4(3)(x+1)
There are 2 types of parabolas. They are
Left right or up down opening ones
Left right ones are in form (y-k)²= 4p(x-h)
Up down ones are (x-h)²=4p(y-k)
In all of them, the vertex is (h, k)
p is the distance from the vertex to the focus, also the shortest distance from the vertex to the directrix making p half of the distance of the shortest path from focus to directrix
If p is positive, then the parabola opens up or right
If p is negative then the parabola opens down or left
If the directrix is y=something, then it is a up down parabola
If directrix is x=something, then it is a left right parabola
Directrix is outside the parabola, kind of at the back
So lets say we had
Focus = (2,3) and directrix is x = -4
Directrix is x =-4 so left right
From x = -4 to x=2 (focus), that is distance of 6
6/2=3
p=3
So, directrix is on opposite side of opening
-4 is to left of the 2
Then the directrix is at back so the parabola opens to the right
p=3, positive 3
Then we have the vertex is halfway between those
So 3 back from focus is from (2,3) to (-1,3)
So vertex is (-1,3)
Equation of a parabola is
(y-3)²= 4(3)(x - (-1))
(y-3)²= 4(3)(x + 1)
Learn more about equation of parabola here: brainly.com/question/3372650
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