SOLUTION: Find the coordinate of the vertices and foci and
the equation of the asymptotes for the hyperbola
with the equation (x+6)^2/36-(y+3)^2/9=1
Algebra.Com
Question 1142079: Find the coordinate of the vertices and foci and
the equation of the asymptotes for the hyperbola
with the equation (x+6)^2/36-(y+3)^2/9=1
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The x^2 term is positive, so the branches open right and left. The general form of the equation for that kind of hyperbola is
In that form, the center is (h,k); a is the distance (in the x direction) from the center to each vertex -- i.e., from the center to each end of the transverse axis; and b is the distance (in the y direction) from the center to each end of the conjugate axis.
With that much information, you can find the coordinates of the center and the two vertices.
The distance (in the x direction) from the center to each focus is c, where .
Now you can find the coordinates of the two foci.
For the asymptotes, set the equation equal to 0 instead of 1 and solve.
The expression on the left is a difference of squares, so it is easy to solve.
The equations of the two asymptotes come from solving the equations
and
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