SOLUTION: Find the equation of parabola with directrix at y=8/3 and focus at (-3/2,4) Use the distance formula to a) find a polynomial equation with integer coefficients for the set o

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of parabola with directrix at y=8/3 and focus at (-3/2,4) Use the distance formula to a) find a polynomial equation with integer coefficients for the set o      Log On


   

Question 1081143: Find the equation of parabola with directrix at y=8/3 and focus at (-3/2,4)

Use the distance formula to
a) find a polynomial equation with integer coefficients for the set of coplanar points/lines described
b) identify the conic; justify your answer. show work
For each point (x,y) its distance from the point (-4,-1) is 3/2 times its distance from the line x=5
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
Set of points (x,y) equally distant from line y=8/3 as from point ( -3/2, 4).

Distance Formula and definition for parabola:


-
%28y-8%2F3%29%5E2=%28x%2B3%2F2%29%5E2%2B%28y-4%29%5E2
y%5E2-16y%2F3%2B64%2F9=%28x%2B3%2F2%29%5E2%2By%5E2-8y%2B16
-16y%2F3%2B64%2F9%2B8y-16=%28x%2B3%2F2%29%5E2
%288-16%2F3%29y%2B64%2F9-16=%28x%2B3%2F2%29%5E2
%28-8%2F3%29y%2B64%2F9-144%2F9=%28x%2B3%2F2%29%5E2
%28-8%2F3%29y=%28x%2B3%2F2%29%5E2%2B80%2F9
y=-%283%2F8%29%28x%2B3%2F2%29%5E2-%283%2F8%29%2880%2F9%29
highlight%28y=-%283%2F8%29%28x%2B3%2F2%29%5E2-10%2F3%29-------Not yet in integer coefficients. Your parts (a) and (b) look like a separate question from the description written above them.


(a)
What is the given information? Same as the description shown before it, or is part of (b) ?


(b)
Follow the description as written and put the information into the Distance Formula. Simplify the equation.

Work with it!

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Find the equation of parabola with directrix at y=8/3 and focus at (-3/2,4)

Use the distance formula to
a) find a polynomial equation with integer coefficients for the set of coplanar points/lines described
b) identify the conic; justify your answer. show work
For each point (x,y) its distance from the point (-4,-1) is 3/2 times its distance from the line x=5
 a)highlight_green%2836x%5E2+%2B+108x+%2B+401+=+96y%29