Question 936512
What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse:
x^2/9 + y^2/16 =1
Given ellipse has a vertical major axis:
Its standard form of equation: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=coordinates of center
..
For given ellipse:
center:(0,0)
a^2=16
a=4
length of major axis=2a=8
b^2=9
b=3
length of minor axis=2b=6
vertices:(0,0±a)=(0,0±4)=(0,-4) and (0,4)
co-vertices:(0±b,0)=(0±3,0)=(-3,0) and (3,0)
foci:
c^2=a^2-b^2=16-9=7
c=√7≈2.6
foci:(0,0±c)=(0,0±2.6)=(0,-2.6) and (0,2.6)