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Chapter 11: Q. 302 (page 1158)

In the following exercises, graph.

(x-2)24-(y-3)216=1

Short Answer

Expert verified

The graph of hyperbola is

Step by step solution

01

Step 1. Given Information

The given equation is(x-2)24-(y-3)216=1

02

Step 2. Explanation 

As x2term is positive, the transverse axis is horizontal. On comparing with the standard form, we get, (h,k)=(2,3).

Thus,

a2=4a=4a=2Andb2=16b=16b=4

Thus, center is (2,3)anda=2,b=4

03

Step 3. Calculation and Graph 

We will find the equation of asymptote as follows,

y=ba(x-h)+ky=42(x-2)+3y=2x-4+3y=2x-1Andy=-ba(x-h)+ky=-42(x-2)+3y=-2x+4+3y=-2x+7

Sketch the asymptote through the diagonal and the vertices on the graph.

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