   Chapter 10.2, Problem 47E

Chapter
Section
Textbook Problem

# Writing a Set of Parametric Equations In Exercises 41–48, use the results of Exercises 37–40 to find a set of parametric equations for the line or conic.Hyperbola: vertices: ( ± ± 5, 0)

To determine

To calculate: A set of parametric equations for the hyperbola whose vertices are (±4,0) and foci are (±5,0).

Explanation

Given:

The vertices of the hyperbola are (±4,0) and foci are (±5,0).

Formula used:

The parametric equation of a hyperbola centered at (h,k) and major axis a and minor axis b is given by:

x=h+asecθ, y=k+btanθ.

Calculation:

According to the provided data, the vertices of the hyperbola are (±4,0) and foci are (±5,0).

Now, since the vertices are provided to be (4,0) and (4,0), so, they are symmetrical to origin, thus, the center of the provided hyperbola is the origin, that is (0,0).

Also, if the center of a hyperbola is at origin, then its vertices is given by:

(a,0) and (a,0).

Thus, the value of a is 4.

Also, the foci of hyperbola is provided to be (±5,0), so the value of c is 5

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