Chapter 10.1, Problem 45E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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. Center : ( 0 ,   0 ) Vertex : ( 0 ,   2 ) Focus : ( 0 ,   4 )

To determine

To calculate: The equation of hyperbola with the Center (0,0), vertex (0,2) and focus (0,4).

Explanation

Given:

The characteristics of hyperbola: center (0,0), vertex (0,2), focus (0,4).

Formula used:

The standard equation of hyperbola,

(yâˆ’k)2a2âˆ’(xâˆ’h)2b2=1

Calculation:

Since the provided equation has y changing vertex in it.

Therefore, the provided hyperbola is of the second type where the transverse axis is the yâˆ’axis.

Now, it is given that the centre of the hyperbola is (0,0) and the distance from the centre to the vertex is 2.

Therefore, the value of a2=4

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