SOLUTION: Write the equation of the hyperbola with a center at (5, 0), vertices along the major axis at (negative-1, 0) and (11, 0), and minor axis with a length of 8.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the hyperbola with a center at (5, 0), vertices along the major axis at (negative-1, 0) and (11, 0), and minor axis with a length of 8.      Log On


   

Question 1079428: Write the equation of the hyperbola with a center at (5, 0), vertices along the major axis at (negative-1, 0) and (11, 0), and minor axis with a length of 8.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Equation of a hyperbola, since the hyperbola has it axis along the x-axis
%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+++=+1+ where (h, k ) is the center and
a = semi-major axis
b = semi-minor axis
if a center at (5, 0), means h=5 and k=0, so we have
%28x-5%29%5E2%2Fa%5E2+-+%28y-0%29%5E2%2Fb%5E2+++=+1+
%28x-5%29%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+++=+1+
it has minor axis length 8, so b+=+8%2F2=4
if vertices along the major axis at (-1, 0) and (11,+0)=> has major axis length 12 (distance from -1 to 11), so major axis a+=+12%2F2=6+
and, your equation is:
%28x-5%29%5E2%2F6%5E2+-+y%5E2%2F4%5E2+++=+1

%28x-5%29%5E2%2F36+-+y%5E2%2F16+++=+1+