Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 10.7, Problem 36E
To determine

Tofind:the graph of the equation and the graph of equation is degenerated case.

Expert Solution & Answer
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Answer to Problem 36E

  x2+y2=0 .

Explanation of Solution

Given:

  (x−2)2+(y−2)2+4(x+y)=8.

Concept used:

The general equation for conic section is:

  Ax2+Bxy+Cy2+Dx+Ey+F=0.

Where A,B,C,D,E and F are constant.

As by changing the values of some of the constants, the shape of the corresponding conic also changes.

If B2−4AC , is less than zero, if a conic exists, it will be either a circle or an ellipse.

If B2−4AC ,equals to zero, if a conic exists, it will be parabola.

If B2−4AC id greater than zero, if a conic exists, it will be hyperbola.

Calculation:

Consider the equation of the conic:

  (x−2)2+(y−2)2+4(x+y)=8.

The general equation in the form of conic:

  Ax2+Bxy+Cy2+Dx+Ey+F=0....(i)

Rearrange the equation in this form as:

  x2−4x+4+y2−4y+4+4x+4y=8.⇒x2+y2=0......(ii)

Comparing equation (i) and (ii) :

  A=1,B=0,C=1,D=0,E=0,F=0.

Now,

  B2−4AC=02−4.1.1=−4.

While B2−4AC<0 and A=C, from the table of comparison of conic, it follows that

  (x−2)2+(y−2)2+4(x+y)=8. represents the circle.

So, write the equation x2+y2=0 in the standard form as:

  (x−0)2+(y−0)2=02....(iii)

The standard equation of an ellipse is:

  (x−h)2+(y−k)2=r2....(iv)

Where (h,k) : center, r:radius .

Compare the equation (iii) and (iv) :

  h=0,k=0,r=0.

Therefore, the equation (iii) describe a point circle with the center (0,0) .

The graph of the equation (x−2)2+(y−2)2+4(x+y)=8 is:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.7, Problem 36E

Hence, the new equation so form is x2+y2=0 .

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Chapter 10.7, Problem 35E
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Chapter 10.7, Problem 37E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFUCh. 10.1 - Prob. 2CFUCh. 10.1 - Prob. 3CFUCh. 10.1 - Prob. 4CFUCh. 10.1 - Prob. 5CFUCh. 10.1 - Prob. 6CFUCh. 10.1 - Prob. 7CFUCh. 10.1 - Prob. 8CFUCh. 10.1 - Prob. 9CFUCh. 10.1 - Prob. 10CFU
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