Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 10.7, Problem 64SR
To determine

To find: The coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation and then graph the hyperbola.

Expert Solution & Answer
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Answer to Problem 64SR

The coordinates of the vertices are (0,2) and (0,−2) , the coordinates of the foci is (0,±8) , the equation of asymptote is y=±13x , and the graph of the hyperbola is shown in figure (1).

Explanation of Solution

Given:

The equation of the hyperbola is 6y2=2x2+12.

Calculation:

Convert the given equation into standard form as follows.

  6y2=2x2+126y2−2x2=12y22−x26=1

The hyperbola is a vertical hyperbola.

Compare the given equation with general equation (y−k)2a2−(x−h)2b2=1 to get (h,k)=(0,0).

  a2=2a=2b2=6=6

Use the relation between a , b and c to compute the value of c as follows.

  c2=a2+b2=2+6=8c=8

Find the coordinates of the vertices of the hyperbola as follows.

  (h,k±a)=(0,0±2)=(0,2) and (0,−2)

Find the coordinates of the foci of the hyperbola as follows.

  (h,k±c)=(0,0±8)=(0,±8)

Find the equation of asymptotes as follows.

  y−k=±ab(x−h)y−0=±26(x−0)y=±13x

The graph of the given parabola is as follows.

  Algebra 2, Chapter 10.7, Problem 64SR

Figure (1)

Therefore, the coordinates of the vertices are (0,2) and (0,−2) , the coordinates of the foci is (0,±8) , the equation of asymptote is y=±13x , and the graph of the hyperbola is shown in figure (1).

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Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
Ch. 10.1 - Prob. 7CYUCh. 10.1 - Prob. 8CYUCh. 10.1 - Prob. 9CYUCh. 10.1 - Prob. 10PPSCh. 10.1 - Prob. 11PPSCh. 10.1 - Prob. 12PPSCh. 10.1 - Prob. 13PPSCh. 10.1 - Prob. 14PPSCh. 10.1 - Prob. 15PPSCh. 10.1 - Prob. 16PPSCh. 10.1 - Prob. 17PPSCh. 10.1 - Prob. 18PPSCh. 10.1 - Prob. 19PPSCh. 10.1 - Prob. 20PPSCh. 10.1 - Prob. 21PPSCh. 10.1 - Prob. 22PPSCh. 10.1 - Prob. 23PPSCh. 10.1 - Prob. 24PPSCh. 10.1 - Prob. 25PPSCh. 10.1 - Prob. 26PPSCh. 10.1 - Prob. 27PPSCh. 10.1 - Prob. 28PPSCh. 10.1 - Prob. 29PPSCh. 10.1 - Prob. 30PPSCh. 10.1 - Prob. 31PPSCh. 10.1 - Prob. 32PPSCh. 10.1 - Prob. 33PPSCh. 10.1 - Prob. 34PPSCh. 10.1 - Prob. 35PPSCh. 10.1 - Prob. 36PPSCh. 10.1 - Prob. 37PPSCh. 10.1 - Prob. 38PPSCh. 10.1 - Prob. 39PPSCh. 10.1 - Prob. 40PPSCh. 10.1 - Prob. 41PPSCh. 10.1 - Prob. 42HPCh. 10.1 - Prob. 43HPCh. 10.1 - Prob. 44HPCh. 10.1 - Prob. 45HPCh. 10.1 - Prob. 46HPCh. 10.1 - Prob. 47STPCh. 10.1 - Prob. 48STPCh. 10.1 - Prob. 49STPCh. 10.1 - Prob. 50STPCh. 10.1 - Prob. 51SRCh. 10.1 - Prob. 52SRCh. 10.1 - 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