What is the equation of an ellipse with vertices 2 0 2 4 and foci 2 1 2 3?
Vertices and the foci lie on the line x =2
Major axis is parellel to the y-axis b > a
Center of the ellipse is the midpoint (h,k) of the vertices
(2,2)
Equation of the ellipse is (x - (2) )^2 / a^2 + (y - (2) )^2 /
b^2
Equation of the ellipse is (x-2)^2 / a^2 + (y-2)^2 / b^2
The distance between the center and one of the vertices is b
The distance between(2,2) and (2,4) is 2, so b = 2
The distance between the center and one of the foci is c
The distance between(2,2) and (2,1) is 1, so c = 1
Now that we know b and c, we can find a^2
c^2=b^2-a^2
(1)^2=(2)^2-a^2
a^2 = 3
The equation of the ellipse is
Equation of the ellipse is (x-2)^2 / 3 + (y-2)^2 / 4 =1