Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12

(x-1)²/64 + (y-2)²/144 = 1

Step-by-step explanation:

The standard equation of an ellipse is expressed as (x-h)²/a² + (y-k)²/b² = 1

Where the coordinate (h,k) is the centre of the ellipse.

a is the the difference of the x coordinates of the centre and the vertex.

b is the minor axis.

Given the centre to be (1,2), on comparing with the coordinate (h,k),

h = 1 and k = 2

The difference of the x coordinates of the centre and the vertex = -7-1 = -8

The minor axis as given in the equation is b = 12

Substituting the given parameters into the equation of an ellipse above we will have;

(x-1)²/(-8)² + (y-2)²/12² = 1

(x-1)²/64 + (y-2)²/144 = 1

The final equation gives the required standard form of the equation of the ellipse.