(a) Given V = (0,0) and Focus, S = (4,0)
It is a right handed parabola with
a = 4 and standard form is y2 = 4ax
Put a = 4, then y2 = 16x.
(b) Given
V = (0,0) and directrix = y = -3
Focus = (0,3) ⇒ a = 3
It is a upward parabola and
standard form is x2 = 4ay
Put a = 3, x2 = 4.3y
⇒ x2 = 12y
(C) Given
Focus = S = (1,0) and directrix is
x =-15 ⇒ a = 1
it is a right handed parabola
and standard form is y2 = 4ax
put a = 1 ⇒ y2 = 4x
(d) Give
Focus = S = (-4, 0) and directrix is
x = 4; S = (-4,0) ⇒ a = 4
It is a left handed parabola standard form is y2 = -4ax
put a = 4
we get y2 = -16x