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Chapter 11: Q. 11.54 (page 1126)

Graphx29-y216=1

Short Answer

Expert verified

The plotted graph ofx29-y216=1is given below

Step by step solution

01

Step 1. Given information

Given that the equation of the hyperbolax29-y216=1.

We need to plot the graph of the given hyperbola.

02

Step 2. Calculations for graphing hyperbola 

The standard form of hyperbola is x29-y216=1. Since term x2 is positive transverse axis is on X-axis and horizontal. Here a2=9soa=卤3, then the vertices -3,0and3,0are on x -axis. Since a=卤3, the rectangle intersects at x-axis and role="math" localid="1645570371884" b=卤4the rectangle intersect at y axis at the points(0,-4)and(0,4). Asymptotes of the given hyperbola is y=43xandy=-43y.

03

Step. 4 Sketching the Graph of hyperbola

The sketched graph of hyperbola using the given information is given below

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