Level of Question: Secondary (12)
Asking question: Student
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- Find the equation of the hyperbola centered at (0,0) with vertices at (0,3) and (0,-3) that is asymptotic to the lines y=+-5x.
- Find the equation of a hyperbola in standard position foci (1,5) and (1,7) and eccentricity 2.
For problem 1 the center being (0,0) and the vertices on the y-axis means that the hyperbola has the form
In this equation when x = 0, y2 = b2, that is y = +-b. But you know that (0,3) and (0,-3) are on the graph and hence b = 3.
I remember that to find the asymptotes of the hyperbola in standard form you factor the left side as a difference of squares.
The two asymptotes are then
This should allow you to find a.
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