Answer:
1)center =(-2,3)
2) Vertices = (8,3) and (-12,3)
3) foci =(4,3) and (-8,3)
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)!