   Chapter 10.1, Problem 44E

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 ) Foci: ( 2 ,   ± 5 )

To determine

To calculate: The equation of hyperbola with the vertices is (2,±3) and foci is (2,±5).

Explanation

Given:

The characteristics of a hyperbola are: vertices is (2,±3) and foci is (2,±5).

Formula used:

The standard equation of parabola 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 (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.

Therefore, a2=9.

Now the standard equation of hyperbola with (h,k) as centre a and b as conjugate and

transverse axis is given by;

(yk)2

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