Question

Find the equation of the parabola with focus at (3,3) and a directrix of y=1

Answer 1

Answer:

−4y

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down.

(x−h)2=4p(y−k)

Find the vertex.

The vertex (h, k) is halfway between the directrix and focus. Find the y coordinate of the vertex using the formula y = y coordinate of focus + directrix 2. The x coordinate will be the same as the x coordinate of the focus.

(3,−1+1

    ___            

      2)

Simplify the vertex.

Add − 1 and 1. (3,0/2) Divide 0 by 2. (3,0).

Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is | p |. Subtract the y coordinate of the vertex from the y coordinate of the focus to find p. p = − 1 − 0 Subtract 0 from − 1 . p = − 1.

Substitute in the known values for the variables into the equation ( x − h ) 2 = 4 p (y − k). (x − 3) 2 = 4 (− 1) (y − 0).

Simplify.

(x − 3) 2= −4y

= −4y