Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
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

774,849 users

Find the standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = 10.

0 votes
asked Aug 7, 2014 in CALCULUS by Tdog79 Pupil

1 Answer

0 votes

The parabola directrix at y = 10 and focus at (0, 10)

The vertical parabola directrix equation is y = k - p

Therfore, the required parabola is horizontal.

Standard form of vertcal parabola is

Where Center (h, k ),focus is (h , k+p ) and directrix is y  = k - p

Directrix y = k - p

k - p = 10 -----> (1)

Focus (h, k+p) = (0, -10)

k + p = -10 ----> (2)

and k = 0

Add the equations (1) & (2).

2k = 0

k = 0

Substitute h value in equation (2).

0+ p = -10

p = -10

Vertex of parabola is (h, k) = (0, 0).

substitute h, k , p values in standard form.

(x-h)^2=4p(y-k)

x^2 =4(-10)(y)

x^2=-40y

Parabola equation is ​x^2=-40y

 

answered Aug 7, 2014 by anonymous

Related questions

...