Find the center, vertices, and foci of the ellipse. simplify your answers as much as possible.

1)center =(-2,3)

2) Vertices = (8,3) and (-12,3)

3) foci =(4,3) and (-8,3)

Step-by-step explanation:

As the general equation of ellipse with center at (h,k) is given by:

(x-h)^2/a^2 +(y-k)^2/b^2 = 1

where a=radius of the ellipse along the x-axis

b=radius of the ellipse along the y-axis

h, k= the x and y coordinates of the center of the ellipse.

Given equation of ellipse:

(x+2)^2/100 + (y-3)^2/64 = 1

1)

Finding center:

comparing with the general formula

h=-2 and k=3

Center of given ellipse is at (-2,3)

2)

Finding vertices:

comparing given equation of ellipse with the general formula:

a^2= 100 and b^2=64

then a = 10 and b=8

As a>b, it means the ellipse is parallel to x-axis

hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)

The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)

3)

Finding Foci, c:

From equations of general ellipse we have a^2 - c^2=b^2

Putting values of a^2=100 and b^2=64 in above

100-c^2=64

c^2=100-64

     = 36

taking square root on both sides

c=6

foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: