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:

Given that

The standard form for an ellipse is

(x-h)/a² + ( y-k)/b²=1

So

h, k

is the centre of the ellipse, and

a is the distance from the centre to the vertices and c is the distance from the centre to the foci.

b is the minor axis.

So b² + c²= a²

In this example

a= -7-1= -8

  q

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.