Question

Find an equation for an ellipse with foci (3,4) and (3,6) and vertices (3,1) and (3,9). _________ = 1

Answer 1

\[(x - h)² /a^2 + (y - k)²/b^2\]
where h.k=(3,5) ----> by mid point formula
now find a and b

Answer 2

we need to define the center that in this case is located at (6-4)/2 = 5=k the center will be at
(3,5). The major axis is parallel to the y axis as we may see for the development of the vertices which move only parallel to the y axis.

Answer 3

Then we have to calculate a, b, c
a is the distance from the center to the vertex along the major axis which becomes (9-1)/2=4
c is the distance from the center to the foci which is (6-4)/2 = 1
we can calculate b which is: c= √(a2-b2) => 1=(16-b2 )=> b2=15
b=√15
Then the equation will be
((x-3)2/16) + ((y-5)/15)= 1

Answer 4

hope it helps!! now