Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
Question
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Chapter 13.6, Problem 3PSA

(a)

To determine

To find: The centre, the radius, the diameter, the circumference and the area of the circle for the given equation.

(a)

Expert Solution
Check Mark

Answer to Problem 3PSA

The centre of the circle is at (0,0) , the radius is 6, the diameter is 12, circumference is 12π and the area is 36π .

Explanation of Solution

Given:

The given equation is x2+y2=36 .

Calculation:

Consider the formula for the equation of the circle is of the form as,

  (xh)2+(yk2)=r2

Here, (h,k) is the centre and r is the radius.

Consider the given equation of the circle is,

  x2+y2=36

From the given equation and the general equation the centre of the circle is,

  (h,k)=(0,0)

The radius of the circle is,

  r2=36r=6

The diameter of the circle is,

  d=2(6)=12

The circumference of the circle is,

  C=πd=12π

The area of the circle is obtained as,

  A=πr2=π(6)2=36π

Thus, the centre of the circle is at (0,0) , the radius is 6, the diameter is 12, circumference is 12π and the area is 36π .

(b)

To determine

To find: The centre, the radius, the diameter, the circumference and the area of the circle for the given equation.

(b)

Expert Solution
Check Mark

Answer to Problem 3PSA

The centre of the circle is at (3,6) , the radius is 10 , the diameter is 20 , circumference is 20π and the area is 100π .

Explanation of Solution

Given:

The given equation is (x3)2+(y+6)2=100 .

Calculation:

Consider the formula for the equation of the circle is of the form as,

  (xh)2+(yk2)=r2

Here, (h,k) is the centre and r is the radius.

Consider the given equation of the circle is,

  (x3)2+(y+6)2=100

From the given equation and the general equation the centre of the circle is,

  (h,k)=(3,6)

The radius of the circle is,

  r2=100r=10

The diameter of the circle is,

  d=2(10)=20

The circumference of the circle is,

  C=dπ=20π

The area of the circle is obtained as,

  A=π(r)2=π(10)2=100π

Thus, the centre of the circle is at (3,6) , the radius is 10 , the diameter is 20 , circumference is 20π and the area is 100π .

(c)

To determine

To find: The centre, the radius, the diameter, the circumference and the area of the circle for the given equation.

(c)

Expert Solution
Check Mark

Answer to Problem 3PSA

The centre of the circle is at (5,0) , the radius is 32 , the diameter is 3 , circumference is 3π and the area is 94π .

Explanation of Solution

Given:

The given equation is (x+5)2+(y)2=94 .

Calculation:

Consider the formula for the equation of the circle is of the form as,

  (xh)2+(yk2)=r2

Here, (h,k) is the centre and r is the radius.

Consider the given equation of the circle is,

  (x+5)2+(y)2=94

From the given equation and the general equation the centre of the circle is,

  (h,k)=(5,0)

The radius of the circle is,

  r2=94r=32

The diameter of the circle is,

  d=2(32)=3

The circumference of the circle is,

  C=dπ=3π

The area of the circle is obtained as,

  A=π(r)2=π(32)2=94π

Thus, the centre of the circle is at (5,0) , the radius is 32 , the diameter is 3 , circumference is 3π and the area is 94π .

(d)

To determine

To find: The centre, the radius, the diameter, the circumference and the area of the circle for the given equation.

(d)

Expert Solution
Check Mark

Answer to Problem 3PSA

The centre of the circle is at (5,2) , the radius is 9 , the diameter is 18 , circumference is 18π and the area is 81π .

Explanation of Solution

Given:

The given equation is (x+5)23+(y2)32=27 .

Calculation:

Consider the formula for the equation of the circle is of the form as,

  (xh)2+(yk2)=r2

Here, (h,k) is the centre and r is the radius.

Consider the given equation of the circle is,

  (x+5)23+(y2)32=27(x+5)2+(y2)=27×3(x+5)2+(y2)2=81

From the given equation and the general equation the centre of the circle is,

  (h,k)=(5,2)

The radius of the circle is,

  r2=81r=9

The diameter of the circle is,

  d=2(9)=18

The circumference of the circle is,

  C=18π=18π

The area of the circle is obtained as,

  A=π(r)2=π(9)2=81π

Thus, the centre of the circle is at (5,2) , the radius is 9 , the diameter is 18 , circumference is 18π and the area is 81π .

Chapter 13 Solutions

Geometry For Enjoyment And Challenge

Ch. 13.1 - Prob. 11PSACh. 13.1 - Prob. 12PSBCh. 13.1 - Prob. 13PSBCh. 13.1 - Prob. 14PSBCh. 13.1 - Prob. 15PSBCh. 13.1 - Prob. 16PSBCh. 13.1 - Prob. 17PSBCh. 13.1 - Prob. 18PSBCh. 13.1 - Prob. 19PSBCh. 13.1 - Prob. 20PSBCh. 13.1 - Prob. 21PSCCh. 13.1 - Prob. 22PSCCh. 13.1 - Prob. 23PSCCh. 13.1 - Prob. 24PSCCh. 13.2 - Prob. 1PSACh. 13.2 - Prob. 2PSACh. 13.2 - Prob. 3PSACh. 13.2 - Prob. 4PSACh. 13.2 - Prob. 5PSACh. 13.2 - Prob. 6PSACh. 13.2 - Prob. 7PSACh. 13.2 - Prob. 8PSACh. 13.2 - Prob. 9PSBCh. 13.2 - Prob. 10PSBCh. 13.2 - Prob. 11PSBCh. 13.2 - Prob. 12PSBCh. 13.2 - Prob. 13PSBCh. 13.2 - Prob. 14PSBCh. 13.2 - Prob. 15PSBCh. 13.2 - Prob. 16PSBCh. 13.2 - Prob. 17PSBCh. 13.2 - Prob. 18PSBCh. 13.2 - Prob. 19PSBCh. 13.2 - Prob. 20PSCCh. 13.2 - Prob. 21PSCCh. 13.2 - Prob. 22PSCCh. 13.2 - Prob. 23PSCCh. 13.2 - Prob. 24PSCCh. 13.2 - Prob. 25PSCCh. 13.2 - Prob. 26PSCCh. 13.2 - Prob. 27PSCCh. 13.3 - Prob. 1PSACh. 13.3 - Prob. 2PSACh. 13.3 - Prob. 3PSACh. 13.3 - Prob. 4PSACh. 13.3 - Prob. 5PSBCh. 13.3 - Prob. 6PSBCh. 13.3 - Prob. 7PSBCh. 13.3 - Prob. 8PSBCh. 13.3 - Prob. 9PSBCh. 13.3 - Prob. 10PSBCh. 13.3 - Prob. 11PSBCh. 13.3 - Prob. 12PSBCh. 13.3 - Prob. 13PSCCh. 13.3 - Prob. 14PSCCh. 13.3 - Prob. 15PSCCh. 13.3 - Prob. 16PSCCh. 13.3 - Prob. 17PSCCh. 13.3 - Prob. 18PSCCh. 13.4 - Prob. 1PSACh. 13.4 - Prob. 2PSACh. 13.4 - Prob. 3PSACh. 13.4 - Prob. 4PSBCh. 13.4 - Prob. 5PSBCh. 13.4 - Prob. 6PSBCh. 13.4 - Prob. 7PSCCh. 13.4 - Prob. 8PSCCh. 13.4 - Prob. 9PSCCh. 13.5 - Prob. 1PSACh. 13.5 - Prob. 2PSACh. 13.5 - Prob. 3PSACh. 13.5 - Prob. 4PSACh. 13.5 - Prob. 5PSACh. 13.5 - Prob. 6PSACh. 13.5 - Prob. 7PSACh. 13.5 - Prob. 8PSACh. 13.5 - Prob. 9PSBCh. 13.5 - Prob. 10PSBCh. 13.5 - Prob. 11PSBCh. 13.5 - Prob. 12PSBCh. 13.5 - Prob. 13PSBCh. 13.5 - Prob. 14PSCCh. 13.5 - Prob. 15PSCCh. 13.5 - Prob. 16PSCCh. 13.5 - Prob. 17PSCCh. 13.6 - Prob. 1PSACh. 13.6 - Prob. 2PSACh. 13.6 - Prob. 3PSACh. 13.6 - Prob. 4PSACh. 13.6 - Prob. 5PSACh. 13.6 - Prob. 6PSACh. 13.6 - Prob. 7PSACh. 13.6 - Prob. 8PSACh. 13.6 - Prob. 9PSACh. 13.6 - Prob. 10PSACh. 13.6 - Prob. 11PSBCh. 13.6 - Prob. 12PSBCh. 13.6 - Prob. 13PSBCh. 13.6 - Prob. 14PSBCh. 13.6 - Prob. 15PSBCh. 13.6 - Prob. 16PSCCh. 13.6 - Prob. 17PSCCh. 13.6 - Prob. 18PSCCh. 13.6 - Prob. 19PSCCh. 13.6 - Prob. 20PSDCh. 13.7 - Prob. 1PSACh. 13.7 - Prob. 2PSACh. 13.7 - Prob. 3PSACh. 13.7 - Prob. 4PSACh. 13.7 - Prob. 5PSACh. 13.7 - Prob. 6PSACh. 13.7 - Prob. 7PSACh. 13.7 - Prob. 8PSACh. 13.7 - Prob. 9PSACh. 13.7 - Prob. 10PSACh. 13.7 - Prob. 11PSACh. 13.7 - Prob. 12PSACh. 13.7 - Prob. 13PSBCh. 13.7 - Prob. 14PSBCh. 13.7 - Prob. 15PSBCh. 13.7 - Prob. 16PSBCh. 13.7 - Prob. 17PSBCh. 13.7 - Prob. 18PSBCh. 13.7 - Prob. 19PSBCh. 13.7 - Prob. 20PSBCh. 13.7 - Prob. 21PSCCh. 13.7 - Prob. 22PSCCh. 13.7 - Prob. 23PSCCh. 13.7 - Prob. 24PSCCh. 13.7 - Prob. 25PSCCh. 13.7 - Prob. 26PSCCh. 13.7 - Prob. 27PSDCh. 13.7 - Prob. 28PSDCh. 13.7 - Prob. 29PSDCh. 13 - Prob. 1RPCh. 13 - Prob. 2RPCh. 13 - Prob. 3RPCh. 13 - Prob. 4RPCh. 13 - Prob. 5RPCh. 13 - Prob. 6RPCh. 13 - Prob. 7RPCh. 13 - Prob. 8RPCh. 13 - Prob. 9RPCh. 13 - Prob. 10RPCh. 13 - Prob. 11RPCh. 13 - Prob. 12RPCh. 13 - Prob. 13RPCh. 13 - Prob. 14RPCh. 13 - Prob. 15RPCh. 13 - Prob. 16RPCh. 13 - Prob. 17RPCh. 13 - Prob. 18RPCh. 13 - Prob. 19RPCh. 13 - Prob. 20RPCh. 13 - Prob. 21RPCh. 13 - Prob. 22RPCh. 13 - Prob. 23RPCh. 13 - Prob. 24RPCh. 13 - Prob. 25RPCh. 13 - Prob. 26RPCh. 13 - Prob. 27RPCh. 13 - Prob. 28RPCh. 13 - Prob. 29RPCh. 13 - Prob. 30RPCh. 13 - Prob. 31RPCh. 13 - Prob. 32RPCh. 13 - Prob. 33RPCh. 13 - Prob. 34RPCh. 13 - Prob. 35RPCh. 13 - Prob. 36RPCh. 13 - Prob. 37RP
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