SOLUTION: How do you find the equation for the hyperbola with a center at( 1,1) an x intercept at (2,0) and one vertex at (5/4, 1) ?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do you find the equation for the hyperbola with a center at( 1,1) an x intercept at (2,0) and one vertex at (5/4, 1) ?      Log On


   

Question 1089559: How do you find the equation for the hyperbola with a center at( 1,1) an x intercept at (2,0) and one vertex at (5/4, 1) ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
find the equation for the hyperbola :%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1
if a center at ( 1,1) =(h,k), we have
%28x-1%29%5E2%2Fa%5E2-%28y-1%29%5E2%2Fb%5E2=1

if an x- intercept at (2,0), we have
%282-1%29%5E2%2Fa%5E2-%280-1%29%5E2%2Fb%5E2=1
1%2Fa%5E2-1%2Fb%5E2=1.....eq.1

and if one vertex at (5%2F4, 1), we have

%285%2F4-1%29%5E2%2Fa%5E2-%281-1%29%5E2%2Fb%5E2=1 ...eq.2 ...solve or a
%285%2F4-4%2F4%29%5E2%2Fa%5E2-0%2Fb%5E2=1
%281%2F4%29%5E2%2Fa%5E2=1
a%5E2=%281%2F16%29

go to
1%2Fa%5E2-1%2Fb%5E2=1.....eq.1 plug in a%5E2=1%2F16 and solve or b
1%2F16-1%2Fb%5E2=1
16-1%2Fb%5E2=1
16-1=1%2Fb%5E2
1%2Fb%5E2=15
b%5E2=1%2F15
your equation is:
%28x-1%29%5E2%2F%281%2F16%29-%28y-1%29%5E2%2F%281%2F15%29=1
16%28x-1%29%5E2-15%28y-1%29%5E2=1