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Chapter 11: Q. 304 (page 1158)

In the following exercises, graph.

(y-1)225-(x-2)29=1

Short Answer

Expert verified

The graph of hyperbola is

Step by step solution

01

Step 1. Given Information

The given equation is(y-1)225-(x-2)29=1

02

Step 2. Explanation 

As y2term is positive, the transverse axis is vertical. On comparing with the standard form, we get, (h,k)=(2,1).

Thus,

a2=25a=25a=5Andb2=9b=9b=3

Thus, center is (2,1)anda=5,b=3

03

Step 3. Calculation and Graph 

We will find the equation of asymptote as follows,

y=ab(x-h)+ky=53(x-2)+1y=53x-103+1y=53x-73Andy=-53(x-2)+1y=-53x+103+1y=-53x+133

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

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