   Chapter 10.1, Problem 38E

Chapter
Section
Textbook Problem

Sketching a Hyperbola In Exercises 37-40, find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using asymptotes as an aid. ( y + 3 ) 2 225 − ( x − 5 ) 2 64 = 1

To determine
The centre, foci, vertices and eccentricity of the provided hyperbola also draw the graph with asymptotes as an aid.

Explanation

Given: The equation of hyperbola, (y+3)2225(x5)264=1

Explanation:

Consider the standard equation of hyperbola, (yk)2a2(xh)2b2=1

Where a represents the transverse axis and b represents the conjugate axis. The ordered pair (h, k) is the centre of the hyperbola.

Thus, for the provided hyperbola, the centre is (5,-3) and the values of a and b are 15 and 8 respectively.

Hence, the vertices of the hyperbola are (5,-3+15) and (5,-3-15)

That is, (5, 12) and (5,-18)

Also, the value of c is given by the formula c2=a2+b2

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