Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,973 users

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

0 votes
asked Aug 4, 2014 in CALCULUS by Tdog79 Pupil

1 Answer

0 votes

The parabola with focus (0,6) and directrix y = - 6

The vertical parabola directrix is in the form y = k - p

So required parabola is vertical.

Standard form of vertical parabola is image

Where image

image

(h, k + p) = (0, 6)

h = 0 and k + p = 6 ---> (1)

The x coordinate of vertex is 0.

And directrix y = -6

k - p = -6  ---> (2)

Add the equations (1) and (2).

2k = 0

k = 0

y coorinate of vertex is 0.

(h, k) = (0,0)

Substitute value of k in equation (1).

0 + p = 6

p = 6

p > 0, the parabola opens upward.

Substitute (h,k) and p in above standard form.

image

The parabola equation is image.

answered Aug 4, 2014 by david Expert

Related questions

...