SOLUTION: Please help me with this problem: Identify and describe the important features of the conic section whose equation is {{{9x^2 - 4y^2 - 36}}} = 0

Algebra ->  Finance -> SOLUTION: Please help me with this problem: Identify and describe the important features of the conic section whose equation is {{{9x^2 - 4y^2 - 36}}} = 0      Log On


   



Question 1008677: Please help me with this problem:
Identify and describe the important features of the conic section whose equation is 9x%5E2+-+4y%5E2+-+36 = 0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E2+-+4y%5E2+-+36=+0
9x%5E2+-+4y%5E2+=+36
9x%5E2%2F36+-+4y%5E2%2F36+=+36%2F36
cross%289%29x%5E2%2Fcross%2836%294+-+cross%284%29y%5E2%2Fcross%2836%299+=+1
x%5E2%2F4+-+y%5E2%2F9+=+1
here you have a hyperbola %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 and h=0,k=0,a=2, and b=3
so, the center is at origin (0,+0)
semi-major axis length:a=+2
semi-minor axis length:b=+3
vertices:
(-a, 0) and (a, 0)
(-2, 0) and (2, 0)

foci:(c, 0) and (-c, 0)
c%5E2=a%5E2%2Bb%5E2
c%5E2=4%2B9
c%5E2=13
c=sqrt%2813%29
(sqrt%2813%29,+0) and (-sqrt%2813%29,+0)
or (3.6,+0) and (-3.6, 0)