Finding the Standard Equation for the Ellipse with Given Vertices and Foci

[iheartmydog]

Homework Statement

Find the equation for the conic ellipse with vertices (-2,-5) (-2, 4) and foci (-2,-4) (-2,3)

Homework Equations

I want to make sure I am solving the problem correctly

The Attempt at a Solution

(x+2)^2/8 + (y+0.5)^2/20.25 =1

 

[symbolipoint]

Here is some help.

Standard equation for the ellipse you describe begins this way:
(x-h)^2/b^2+(y-k)^2/a^2=1,
and a is the semi-major axis length, and a>b. You gave focus points which are on the line, x=-2, and so consistent with the given major axis being vertical. Checking the vertices you find the value for a is |-5-(4)|*(1/2)=4.5,
a=4.5

You also find that based on the foci, the center of your ellipse is at x=-2 and y=(-4+3)*(1/2)=-(1/2); or the point for center is (-2, -1/2).There is a fairly well known relationship between a, c, and the minor axis length b. I leave finding this and the rest of the work to you. A review from a college algebra or intermediate algebra textbook will be very helpful. Give a try first before more help is given - if any needed.

Checking your results again, it seems you mostly or entirely have the right idea; your center point reads correctly in your equation, at least.