x^2/144+y^2/25=1
The largest denominator is a^2 and the smallest denominator is b^2, then:
a^2=144→sqrt(a^2)=sqrt(144)→a=12
b^2=25→sqrt(b^2)=sqrt(25)→b=5
The equation is of the form:
x^2/a^2+y^2/b^2=1
This is an ellipse with center C=(h,k) at the Origin → C=(0,0) and major axis on the x-axis and minor axis on the y-axis.
The vertices have coordinates:
V'=(-a,0) and V=(a,0)
Replacing a=12
V'=(-12,0) and V=(12,0)
The foci have coordinates:
F'=(-c,0) and F=(c,0)
c^2=a^2-b^2
c^2=144-25
c^2=119
sqrt(c^2)=sqrt(119)
c=sqrt(119)
Then the coordinates of the foci are:
F'=(-sqrt(119),0) and F=(sqrt(119),0)
Answers:
Centrer: C=(0,0)
Vertices: V'=(-12,0) and V=(12,0)
Foci: F'=(-sqrt(119),0) and V=(sqrt(119),0)