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Conic Sections - Hyperbola


The standard equation for hyperbolas is:

where b2 = c2 - a2

vertices (± a,0) (0, ± a)foci (± c,0) (0, ± c)transverseaxis on x-axis, on y-axis,length 2a length 2aconjugateaxis on y-axis, on x-axis,length 2b length 2b

a is always larger than b; and a,b, and c are related by c2 = a2 + b2

Graph 9x2 - 16y2= 144

a2 = 16 ; b2 = 9
major axis: x-axis
vertices: (± 4,0)

c2 = a+ b
c2 = 16 + 9
c2 = 25

foci: (± 5,0)


Graph 36x2 - 4y2 + 144 = 0
36x2 - 4y2 = -144 factor -1 out
4y2 - 36x2 = 144

a2 = 36 ; b2 = 4
major axis: y-axis
vertices: (0,± 6)

c2= a2 + b2
c2= 36 + 4
c2 = 40

(to find the asymptotes, let the x term equal the y term and solve for y)

Subject X2: 

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