Find the standard form of the equation of the ellipse

Question

Find the standard form of the equation of the ellipse with the given characteristics.

Center: (1, 2); vertex: (−5, 2); minor axis of length 6

I have tried twice and failed, could anyone help me?

Answer 1

I bet your problem has been with the term minor axis. Note that this is twice the distance from the center to the edge of the ellipse on the minor axis; this is the value referred to in the ellipse equation.

Thus, as 1 - -5 = 6, the equation of the ellipse is (x-1)^2/6^2 +(y-2)^2/3^2 = 1, or

(x-1)^2/36 +(y-2)^2/9 = 1

Answer 2

Since your ellipse center is (h, k)=(1,2) and one vertex is (-5,2) you can conclude that the other vertex is (7,2) which tells you that a=6.

Since minor axis length is 6 you can conclude that Co-Vertices are (1,-1) and (1,5) therefore b=3.

Now that you know a and b you can write your ellipse equation which is (x-h)^2/a^2+(y-k)^2/b^2 =1 or (x-1)^2/36+ (y-2)^2/9=1