The equation (x-6)^2/16 + (y+7)^2/4 = 1 represents an ellipse. what are the vertices of the ellipse? a.) (6, –3) and (6, –11) b.) 6, –5) and (6, –9) c.) (10, –7) and (2, –7) , –7) and (4, –7)

The correct option is C.

Step-by-step explanation:

The given equation is

It can be rewritten as

        .....(1)

The standard form of an ellipse is

          ....(2)

Where (h,k) is center of the ellipse.

If a>b, then the vertices of the ellipse are .

From (1) and (2) we get

Since a>b, therefore the vertices of the ellipse are

The vertices of the given ellipse are (10, –7) and (2, –7). Therefore the correct option is C.