SOLUTION: Find equation for the ellipse that shares a vertex and focus with the parabola x^2 + y = 100 and has its other focus at the origin? I know what the shape of the two figures toge

Algebra.Com
Question 451902: Find equation for the ellipse that shares a vertex and focus with the parabola x^2 + y = 100 and has its other focus at the origin?
I know what the shape of the two figures together would look like, and i found that 2C is 100, since that is the distance between foci. From that I determined that 2b - c = 100. What I don't get is how to find a and b. Thanks very much!
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
You say that the ellipse shares a vertex (the point (0, 100)) and a focus with the parabola , or , or . Hence for the parabola, the distance from the vertex to the focus is 1/4. Also, one focus of the ellipse must be (0, 399/4). It was given that the other focus of the ellipse is (0,0) (the origin). The center of the ellipse is then the point (0, 399/8). So
, and .
Then
Then the standard equation is
, or
.
RELATED QUESTIONS

A parabola has its focus at (7, -4) and directrix Y = 2. Find the... (answered by ewatrrr)
Find the equation for a parabola with its focus at (5,0) and with directrix x=-5 (answered by Edwin McCravy)
Find the vertex, focus, and directrix of the parabola with equation... (answered by Edwin McCravy)
Find an equation for the parabola that has its vertex at the origin and has a focus at... (answered by josgarithmetic)
help me find the equation of the parabola with its vertex at (-1, 2) and its focus at (4, (answered by ewatrrr)
1. Find the standard form of the equation of the parabola with a focus at (0, -9) and a... (answered by josgarithmetic)
Find an equation for the parabola that has its vertex at the origin and has its focus at (answered by MathLover1)
An ellipse has a vertex at (4,4) And a covertex at (2,5). Please find its equation in... (answered by lwsshak3)
A.) What is an equation of the parabola with vertex at the origin and focus (-5,0)? (answered by lwsshak3)