SOLUTION: A hyperbola has center (0,0) and one vertex A(√6 , 0) a) find the equation if fit passed through J(9,5) b) find the value of x if K(x,2) is on the hyperbola c) find the

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A hyperbola has center (0,0) and one vertex A(√6 , 0) a) find the equation if fit passed through J(9,5) b) find the value of x if K(x,2) is on the hyperbola c) find the       Log On


   

Question 824639: A hyperbola has center (0,0) and one vertex A(√6 , 0)
a) find the equation if fit passed through J(9,5)
b) find the value of x if K(x,2) is on the hyperbola
c) find the value of y if I(3,y) is on the hyperbola
Thanks so much in advance:)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A hyperbola has center (0,0) and one vertex A(√6 , 0)
a) find the equation if fit passed through J(9,5)
b) find the value of x if K(x,2) is on the hyperbola
c) find the value of y if I(3,y) is on the hyperbola
***
Hyperbola has a horizontal transverse axis with center at the origin.
Its standard form of equation: x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1
..
a=√6
a^2=6
..
a) solving for b^2:
9%5E2%2F6-5%5E2%2Fb%5E2=1
81%2F6-25%2Fb%5E2=1
25%2Fb%5E2=81%2F6-1
25%2Fb%5E2=75%2F6
b^2=(6)(25)/75=2
Equation:
x%5E2%2F6-y%5E2%2F2=1
..
b)x%5E2%2F6-2%5E2%2F2=1
x%5E2%2F6-4%2F2=1
x^2/6=3
x^2=18
x=±√18=±4.2426
..
c)3%5E2%2F6-y%5E2%2F2=1
9%2F6-y%5E2%2F2=1
y^2/2=9/6-1=3/6
y^2=1
y=±1