SOLUTION: Opens to the right, length of the latus rectum = 6, and passing through (2/3, 0) and (- 1/2, 7)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Opens to the right, length of the latus rectum = 6, and passing through (2/3, 0) and (- 1/2, 7)      Log On


   

Question 1202880: Opens to the right, length of the latus rectum = 6, and passing through
(2/3, 0) and (- 1/2, 7)
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Opens to the right, length of the latus rectum = 6, and passing through
(2/3, 0) and (- 1/2, 7)
Parabola opening right has p > 0, equation

%28y-k%29%5E2=4p%28x-h%29%5E%22%22

latus rectum = 4p = 6

Substitute (x,y) = %28matrix%281%2C3%2C2%2F3%2C%22%2C%22%2C0%29%29

%280-k%29%5E2=6%282%2F3-h%29%5E%22%22
k%5E2=4-6h%29
6h=4-k%5E2

Substitute (x,y) = %28matrix%281%2C3%2C-1%2F2%2C%22%2C%22%2C7%29%29

%287-k%29%5E2=6%28-1%2F2-h%29

49-14k%2Bk%5E2=-3-6h%0D%0A%7B%7B%7B6h=-52%2B14k-k%5E2%29

Equating expressions for 6h

4-k%5E2=-52%2B14k-k%5E2
4=-52%2B14k
56=14k
4=k
Substitute in 6h=4-k%5E2
6h=4-4%5E2
6h=4-16
6h=-12
h=-2

Equation is:

%28y-4%29%5E2=6%28x-%28-2%29%5E%22%22%29
%28y-4%29%5E2=6%28x%2B2%5E%22%22%29



Edwin