SOLUTION: What are the slopes of the asymptotes of a hyperbola with equation (y - 2) squared/ 1 squared - (x- 4) squared/ 3 squared = 1?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What are the slopes of the asymptotes of a hyperbola with equation (y - 2) squared/ 1 squared - (x- 4) squared/ 3 squared = 1?       Log On


   

Question 629767: What are the slopes of the asymptotes of a hyperbola with equation (y - 2) squared/ 1 squared - (x- 4) squared/ 3 squared = 1?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28y+-+2%29%5E2%2F1%5E2+-+%28x-+4%29%5E2%2F3%5E2+=+1
The slopes of the asymptotes of a hyperbola are either +a%2Fb or +b%2Fa. If you're like me you have trouble which one to use when. This can be figured out, as you'll see shortly.

From the equation we can tell that
  • a = 1 (since a%5E2 is always under the first term)
  • b = 3 (since b%5E2 is always under the first term)
  • the hyperbola is vertically oriented (since the the first term has "y", not "x", in it).
On a vertically oriented hyperbola, the a will be a vertical distance (IOW a "rise") and the b will be a horizontal distance (IOW, a "run"). Since slope is always rise/run we will need to use +a%2Fb for this hyperbola.

So the slopes of this particular hyperbola are +1%2F3