SOLUTION: Find the coordinates of the foci, the endpoints of the major axis, minor axis and the latus rectum. x^2/169+y^2/144=1

Algebra ->  Finance -> SOLUTION: Find the coordinates of the foci, the endpoints of the major axis, minor axis and the latus rectum. x^2/169+y^2/144=1      Log On


   



Question 1190890: Find the coordinates of the foci, the endpoints of the major axis, minor axis and the latus rectum.
x^2/169+y^2/144=1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
x%5E2%2F169%2By%5E2%2F144=1-> this is an ellipse
compare to standard form %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 and you see that
h=0 and k=0
a%5E2=169->a=13
b%5E2=144->b=12
c=sqrt%2813%5E2-12%5E2%29
c=sqrt%2825%29
c=5
the coordinates of the foci: (h%2Bc,k) and (h-c,k)
since h=0 and k=0, foci are at (c,0) and (-c,0)
so, foci are at: (5, 0) and (-5, 0)
the major axis: 2a=26
minor axis: 2b=24
the endpoints of the major axis are at vertices : (a,0) and (-a,0)
(13,0) and (-13,0)
the endpoints of the minor axis are at co-vertices : (0,b) and (0,-b)
(0,12) and (0,-12)
the latus rectum:
latus rectum of an ellipse is nothing but 2b%5E2%2Fa
%282%2A12%5E2%29%2F13=288%2F13=22.15