Answer:
(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.
