Question

Write equation of the hyperbola which satisfies the given conditions:
A.) C(0,0) transverse axis along the x-axis, a focus at (5,0) transverse axis=6.
B.) C(1,-2) transverse axis parallel to the x-axis, transverse axis 6, conjugate axis 10.
C.) C(0,0) transverse axis along the y-axis passing through the points (5,3) and (-3,2).
D.) C(0,6), conjugate axis along the y-axis, asymptotes are 6x-5y+30 and 6x+5y-30=0

Answer 1

You really should review your conic sections, and at least show some effort here.
#A.
c = 5
a = 3 (transverse axis = major axis)
so, b = 4 (conjugate semi-axis)
x^2/9 - y^2/16 = 1

#B. very similar to #A. See what you can do.

#3. You know the equation is
y^2/a^2 - x^2/b^2 = 1
so plug in your points and solve for a,b

#D. the asymptotes have slope b/a. So,
b = 6
a = 5
x^2/25 - (y-6)^2/36 = 1