Question

Find the equation of the parabola given that its. 

(a) Vertex is (0,0) and focus is (4,0) 

(b) Vertex is (0,0) and directrix is y = – 3 

(c) Focus is (1,0) and directrix is x = – 1, 

(d) Focus is (-4, 0) and directrix is x = 4

Answer 1

(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