SOLUTION: find the coordinates of the centre, foci, vertices and the equation of the asymptotes then graph the equation: {{{x^2 -y^2 =8x -12}}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: find the coordinates of the centre, foci, vertices and the equation of the asymptotes then graph the equation: {{{x^2 -y^2 =8x -12}}}      Log On


   

Question 874059: find the coordinates of the centre, foci, vertices and the equation of the asymptotes then graph the equation:
x%5E2+-y%5E2+=8x+-12
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-y%5E2+=8x+-12
x%5E2+-8x++-y%5E2+=-12
%28x-4%29%5E2+-+y%5E2+=+4+
%28x-4%29%5E2%2F2%5E2+-+y%5E2%2F4+=+1+
centre (4,0)
vertices (2,0) and (6,0)
foci c = sqrt%288%29 (2+2√2, 0) and (2-2√2, 0)
equation of the asymptotes: m = ± 1, y = 4x + 4, y = -4x - 4
Standard Form of an Equation of an Hyperbola opening right and left is:
%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 with C(h,k) and vertices 'a' units right and left of center, 2a the length of the transverse axis. e = c/a.
Foci are sqrt%28a%5E2%2Bb%5E2%29 = c- units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a