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Question 1163243: Write the equation of the hyperbola:
Vertex at the origin, Passes through 5,10. Axis: x axis
(That is all the information given.)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
That is not enough information to determine a unique hyperbola.
With the (transverse) axis on the x-axis, the general equation is
where (h,k) is the center of the hyperbola.
The parameter a is the distance from the center of the hyperbola to each vertex. So with one vertex at the origin, and with the hyperbola passing through (5,10), the center of the hyperbola is at (-a,0). And then the equation is
Using the given point (5,10), you can choose any (positive) value you want for a and determine the corresponding value of b; every different value of a will result in a different value for b; and that means every different value of a will give a different hyperbola that satisfies the conditions of the problem.
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