SOLUTION: Determine the equation of the hyperbola whose asymptotes are x�2y=0 and which passes through (4,3)

Question 758896: Determine the equation of the hyperbola whose asymptotes are x�2y=0 and which passes through (4,3)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Determine the equation of the hyperbola whose asymptotes are x�2y=0 and which passes through (4,3)
***
Hyperbola has a vertical transverse axis since it passes thru (4,3)
Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center
Asymptotes are two straight line equations that intersect at center, y=mx+b, m=slope, b=y-intercept
Equation of asymptote with positive slope:
x-2y=0
2y=x
y=x/2
m=1/2, b=0
..
Equation of asymptote with negative slope:
x+2y=0
2y=-x
y=-x/2
m=-1/2, b=0
This means center is at (0,0)
..
slopes of asymptotes with vertical transverse axis
=�a/b=�1/2
b=�2a
b^2=4a^2
..
solving for a^2 and b^2 using coordinates of given point(4,3)
(y-k)^2/a^2-(x-h)^2/b^2=1
y^2/a^2-x^2/4a^2=1
9/a^2-16/4a^2=1
9/a^2-4/a^2=1
5/a^2=1
a^2=5
b^2=4a^2=20
Equation:
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