SOLUTION: I'm in dire need of help on my Honors pre-calculus assignment. I'm given the foci (3,+-2) and the x intercepts of -1 and 7 . How do I find the equation of the conic (parabola

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I'm in dire need of help on my Honors pre-calculus assignment. I'm given the foci (3,+-2) and the x intercepts of -1 and 7 . How do I find the equation of the conic (parabola      Log On


   

Question 240467: I'm in dire need of help on my Honors pre-calculus assignment.
I'm given the foci (3,+-2) and the x intercepts of -1 and 7 .
How do I find the equation of the conic (parabola, hyperbola, or ellipse) described?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
there are two foci, in a VERTICAL line, symmetric about the x-axis

if this were a hyperbola, there would be NO x-intercepts

so you have an ellipse
___ centered at (3,0)
___ the length of the minor axis is ___ 2b = 7 - -1 = 8 ___ so, b = 4
___ distance from center to focus (c) is 2
___ a^2 = b^2 + c^2 = 16 + 4 = 20

[(x - 3)^2 / 16] + [(y - 0)^2 / 20] = 1