   Chapter 10.1, Problem 43E

Chapter
Section
Textbook Problem

# Finding the Standard Equation of a Hyperbola In Exercises 41–48, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: ( 2,   ±3 ) Point   on   graph: ( 0 ,   5 )

To determine

To calculate: The equation of hyperbola with the characteristics vertex is (2,±3) and point on the graph is (0,5).

Explanation

Given:

The characteristics for a hyperbola with vertex at (2,±3) and point on the graph is (0,5).

Formula used:

The standard equation of the hyperbola is,

(yk)2a2(xh)2b2=1

Calculation:

Since the given equation has y changing vertices in it,

Therefore, it’s a hyperbola of the second type (i.e. where the transverse axis is the yaxis)

Now, the mid-point of both the vertices gives us the centre of the hyperbola is (2,0) and the distance from centre to the vertex is 3 such that a2=9

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