Question 486333: please help me finish this hyperbola: this is what it gives me.
The hyperbola with center at (5, -6), with vertices at (0, -6) and (10, -6), with (15, 0) a point on the hyperbola.
here is the equation setup:
( )^2/( )-( )^2/( )=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The hyperbola with center at (5, -6), with vertices at (0, -6) and (10, -6), with (15, 0) a point on the hyperbola. Here is the equation setup: ( )^2/( )-( )^2/( )=1
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The given equation is that of a hyperbola with horizontal transverse axis of the standard form:
(x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
..
For given equation:
Center: (5,-6) (given)
length of horizontal transverse axis=10-0=10=2a
a=5
a^2=25
..
Solving for b^2
Using given point (15,0) on hyperbola
(15-5)^2/25-(0+6)^2/b^2=1
100/25-36/b^2=1
4-36/b^2=1
36/b^2=3
b^2=36/3=12
...
Equation:
(x-5)^2/25-(y+6)^2/12=1
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