FIND THE EQUATION OF ELLIPSE FROM VERTICES AND ENDPOINTS

Problem 1 :

Vertices: (5, 0), (5, 12)

endpoints of the minor axis: (1, 6), (9, 6)

Solution:

The symmetric is about y-axis. 

Minor axis = 2b

minor axis: (1, 6), (9, 6)

Major axis = 2a

Vertices: (5, 0), (5, 12)

The midpoint of vertices is the center of the ellipse

The equation of the ellipse is

Problem 2 :

Vertices: (0, 2), (4, 2)

endpoints of the minor axis: (2, 3), (2, 1)

Solution:

The symmetric is about x-axis. 

Minor axis = 2b

minor axis: (2, 3), (2, 1)

Major axis = 2a

Vertices: (0, 2), (4, 2)

The midpoint of vertices is the center of the ellipse

The equation of the ellipse is

Problem 3 :

Major axis vertical with length 10

Length of minor axis 4; Center (-2, 3)

Solution:

Major axis is vertical

Center (h, k) = (-2, 3)

Major axis = 2a

Minor axis = 2b

2a = 10

a = 5

2b = 4

b = 4

So, the equation of an ellipse is

Problem 4 :

Endpoints of Major axis: (7, 9) & (7, 3)

Endpoints of Minor axis: (5, 6) & (9, 6)

Solution:

Major axis: (7, 9) (7, 3)

Major axis = 2a

Minor axis = 2b

So, equation of ellipse is