   Chapter 10.5, Problem 21E

Chapter
Section
Textbook Problem

# Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.21. x2 − y2 = 100

To determine

To Find: The vertices, foci and asymptotes of the hyperbola for the equation x2y2=100.

Explanation

Given:

The hyperbola equation is as follows.

x2y2=100 (1).

Divide the equation (1) with the value 100.

x2100y2100=100100

x2100y2100=1 (2).

Then, compare the equation (2) with the standard equation of hyperbola,

x2a2y2b2=1

Calculation:

Compute the center of the hyperbola using the equation.

(xh)2a2+(yk)2b2=1(x0)2100+(y0)2100=1

Therefore, the center of the hyperbola (h,k) is (0,0)_.

Substitute the value 36 for a2 and 64 for b2 in equation (2).

a2=100a=100a=10

b2=100b=100b=10

Compute the vertices.

vertices=((h±a),k)

Substitute the value 0 for h,0 for k and 10 for a.

vertices=((0±10),0)

Then, the vertices of the hyperbola are (±10,0)_.

Compute the value of c using the equation below.

c2=a2+b2

Substitute the value 10 for a and 10 for b.

c2=(10)2+(10)2c2=100+100c=200c=102

Compute the foci

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