SOLUTION: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (±2, 0); foci: (±3, 0)

Question 1176575: Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices: (±2, 0); foci: (±3, 0)

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

There are two standard forms:
1.
2.

Foci is given to be, (, ) and (, ), tells us that the hyperbola is the horizontal transverse type with the equation in item 1

.... since the center is half way between foci, so it is at origin; so, and

The distance to the focus is linear eccentricity .
The point (, ) shows us the value of :
The distance to the Vertices is .
The point (, ) shows us the value of

then your equation is:

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