SOLUTION: Find the hyperbola equation with Center (6,0) , focal axis parallel to the x axis, and asymptotes 5x-6y-30=0, 5x+6y-30=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the hyperbola equation with Center (6,0) , focal axis parallel to the x axis, and asymptotes 5x-6y-30=0, 5x+6y-30=0      Log On


   



Question 1132595: Find the hyperbola equation with Center (6,0) ,
focal axis parallel to the x axis, and asymptotes 5x-6y-30=0, 5x+6y-30=0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the hyperbola equation with Center (6,0) ,
focal axis parallel to the x axis, and asymptotes 5x-6y-30=0, 5x%2B6y-30=0
general formula:
%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2++=1+
with Center (6,0)

%28x-6%29%5E2%2Fa%5E2-%28y-0%29%5E2%2Fb%5E2++=1

%28x-6%29%5E2%2Fa%5E2-y%5E2%2Fb%5E2++=1
recall:
center: (h,k)
foci:( h+-c, k)
vertices: (h+-a, k)
equation of transverse axis: y=k
The equations of the asymptotes of any hyperbola can be determined by a
translation of the graph to a center at (h, k).
y+-k%28b%2Fa%29%28x+-h%29

if asymptotes:
5x-6y-30=0 =>6y=5x-30=>y=%285%2F6%29x-6
5x%2B6y-30=0 =>6y=-5x%2B30=>y=-%285%2F6%29x%2B6
=>%28b%2Fa%29=%285%2F6%29
=>b=5 and a=6

so, your equation is:
%28x-6%29%5E2%2F6%5E2-y%5E2%2F5%5E2++=1