SOLUTION: Find the equation of the ellipse with a vertex at (4,10), and foci at (4,2) and (4,8)

Question 955294: Find the equation of the ellipse with a vertex at (4,10), and foci at (4,2) and (4,8)
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The foci allow finding the center, and then that one given vertex lets you know value for variable a.

CENTER: On line x=4, y value is .

Note that foci are in a vertical arrangement so "a" goes under the y-rational expression. .

Currently we have a=5 and .

, from the graph and derivation of an ellipse with vertical axis of symmetry or either horizontal axis of symmetry.
How far is center from either focus? .
What was a? .
Find b.

Finish the equation:

RELATED QUESTIONS
Find the equation of the ellipse with foci (2,-4) and (2,8) and with a vertex at (2,10) (answered by lwsshak3)

Find the equation of the ellipse if the vertex is at (5,1) and foci at (-2,1) and (4,1).... (answered by greenestamps)

find the equation of the ellipse if the vertex is at (5,1) and foci at (-2,1) and (4,1).... (answered by CPhill)

Find the equation of the ellipse with foci at (-4,0) and (-4,6) and vertex at... (answered by robertb)

find the equation of the ellipse , eccentricity = 4/5 , a centre at (0,0) and foci... (answered by josgarithmetic)

Find an equation for an ellipse with major axis of length 10 and foci at (0,-4) and... (answered by lwsshak3)

Find the equation of the ellipse with the following properties. The ellipse with foci... (answered by solver91311)

Write an equation in standard form of the ellipse described. Foci at (8, 2) and (2, 2);... (answered by Edwin McCravy)

Which of these descriptions of ellipses matches this equation? The ellipse is centered on (answered by ikleyn)