SOLUTION: Find the equation of the hyperbola that satisfies the given conditions:
Vertex at (6,5)
Conjugate axis along x-axis
Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0
Algebra ->
Quadratic-relations-and-conic-sections
-> SOLUTION: Find the equation of the hyperbola that satisfies the given conditions:
Vertex at (6,5)
Conjugate axis along x-axis
Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0
Log On
Question 826183: Find the equation of the hyperbola that satisfies the given conditions:
Vertex at (6,5)
Conjugate axis along x-axis
Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the equation of the hyperbola that satisfies the given conditions:
Vertex at (6,5)
Conjugate axis along x-axis
Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0
***
hyperbola has a vertical transverse axis
Its standard form of equation:
..
5x-6y-30=0
6y=5x-30
y=5x/6-5
..
5x+6y-30=0
6y=-5x+30
y=-5x/6+5
slopes of asymptotes=±5/6
..
for hyperbolas with a vertical transverse axis, slopes of asymptotes=±a/b=±5/6
b=±(6/5)a
a=±5
a^2=25
b=±(6/5)a=6
b^2=36
..
asymptotes intersect at center of hyperbola:
5x-6y-30=0
5x+6y-30=0
add:
10x-60=0
10x=60
x=6
6y=5x-30
6y=30-30=0
y=0
center: (6,0)
equation of hyperbola:
..
(