Question 668706
find the foci and vertices of the ellipse.
x^2 y^2
--+ --=1
144 169
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Standard form of equation for an ellipse with vertical major axis: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}
a>b, (h,k)=(x,y) coordinates of the center
For given equation: {{{(x)^2/144+(y)^2/169=1}}}
center: (0,0)
a^2=169
a=√169=13
vertices:(0,0±a)=(0,±13)=(0,-13) and (0,13)
b^2=144
b=√144=12
c^2=a^2-b^2=169-144=25
c=√25=5
Foci:(0,0±c)=(0,±5)=(0,-5) and (0,5)