Write the standard form of the equation of the parabola with the given focus of (2,0) and vertex of (0,0)

Question

 Original question: "Write the standard form of the equation of the parabola with the given focus and vertex at (0,0). 

1.) (2,0)

2.) (0,1)

3.) (-1,0)

4.) (0,1/2)

5.) (3,0)

6.) (o,-6)

Answer 1

Since the focus is above the vertex this parabola opens upward.

The standard form of the equation is

y = ax² + bx + c

The vertex form is found by

(x-h)² = 4p(y-k)

 

(h,k) is the vertex.... in this case (h,k) = (0,0)

p = distance from vertex to focus or the distance from (0,0) to (2,0) so p = 2

 

Plugging in to the vertex form we get:

(x-0)² = 4(2)(y-0)

x² = 8y

 

For standard form simply solve for y

 

y = (1/8)x²