Question 770449: Find the equation of the hyperbola whose centre is (1, 0), one focus is (6, 0) and transverse axis 6.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! With the center at (1,0) and a focus 5 units to the right, at (6,0), you know that the focal distance is  anf that the transverse axis is along the x-axis.
(You also know that the other focus will be 5 units to the left of the center, at (4,0), and that is useful if you need to sketch the hyperbola).
The equation of a hyperbola with a transverse axis parallel to the x-axis and center at (h,k) is
In this case, since the center is (1,0), the equation is
We need to find  and  .
is the distance from a vertex to the center, half of the length of the transverse axis.
If the transverse axis is 6, the vertices are 6 units apart,
and they are  units from the center.
(If you need to sketch the hyperbola, the vertices are 3 units to the right and 3 units to the left of the center, at (-2,0) and (4,0)).
The other number you need for the equation of the hyperbola is such that
 .
So  --> --> --> -->
So the equation of the hyperbola in question is
 or 
|
|
|
