mathematics

Here's one example of how settlement and EQUAL CIRCLES SET ...

 PROBLEM1. Consider the following set of Cartesian plane.a. {(X, y) │ x2 + y2 = 16}b. {(X, y) │ x2 + y2 <16}c. {(X, y) │ x2 + y2> 16}
2. Write the equation of a circle with center O and radius:a. 5 b. 10 c. 7 d. 1.5
3. Find the equation of a circle with center O and through the point:a. (3.2) b. (-2.7) C. (5.0) d. (-4, -3)
4. Find the radius of the circle following:a. x2 + y2 = 81b. x2 + y2 = 32c. 2x2 +2 y2 = 36d 4x2 +4 y2 = 9
5. Determine the value of m if a given point lies on the circle besidea. (-2, m), x2 + y2 = 13b. (m, -5), x2 + y2 = 41c. (m, 7), x2 + y2 = 58

ANSWER1.[(X, y) I x2 + y2 = 16]Center at the point (0,0) and berjari2 r = √ 16 = 4Not yet
Not yet
2.5X2 + y2 = 52 or x2 + y2 = 2510thX2 + y2 = 102 or x2 + y2 = 1007X2 + y2 = 72 or x2 + y2 = 491.5X2 + y2 = 1.52 or x2 + y2 = 2.25


3.a) the center point O = (0,0) and passes through the point (3,2)replied: r2 = x2 + y2= (3) 2 + (2) 2= 9 +4= 13 x2 + y2 = 13
b) the center point O = (0,0) and passes through the point (-2.7)replied: r2 = x2 + y2= (-2) 2 + (7) 2= 4 +49= 53 x2 + y2 = 53
                             c) the center point O = (0,0) and passes through the point (5,0)replied: r2 = x2 + y2= (5) 2 + (0) 2= 25 +0= 25 x2 + y2 = 25 or x2 + y2 = 52
               d) the center point O = (0,0) and passes through the point (-4, -3)replied: r2 = x2 + y2= (-4) 2 + (-3) 2= 16 +9= 25 x2 + y2 = 25 or x2 + y2 = 524. a. x2 + y2 = 81Titk center (0,0) and radius r = √ 81 = 9
b. x2 + y2 = 32Central point (0,0) and radius r = √ 32 = 2 √ 8

               c. 2x2 +2 y2 = 36
   Central point (0,0) and radius r = √ 36 = 6
d. 4x2 +4 y2 = 9Central point (0,0) and radius r = √ 9 = 35. a. (-2, M), x2 + y2 = 13(-2, M), x2 + y2 = 13(-2) 2 + m2 = 134 + m2 = 13m2 = 13-4m2 = 9m = √ 9m = 3b. (M, -5), x2 + y2 = 41(M, -5), x2 + y2 = 41m2 + (-5) 2 = 41m2 + 25 = 41m2 = 41-25m2 = 16m = √ 16m = 4

c. (M, 7), x2 + y2 = 58m, 7), x2 + y2 = 58m2 + (7) 2 = 58m2 + 49 = 58m2 = 58-49m2 = 9m = √ 9m = 3



        EXERCISE 2
1. Find the equation of the circle with center and radius of the following:a. (2.2), 3b. (0.5), 4c. (-5.2), 6d. (2, -3), 4e. (-4, -3), 5f. (-6.6) 2
2. Write the equation of the circle:a. Based in (8.6) and through Ob. Centered at (-1.1) and by (3.3)c. Centered at (-2.0) and by (4.3)d. Based in (8, -15) and through O
3. Determine the center and radius of the following circle;a. x2 + y2 - 2x - 6y +6 = 9b. x2 + y2 - 4x - 4y = 0c. x2 + y2 + 6x = 0d. x2 + y2 + 4x - 4y + 7 = 0e. x2 + y2 + 8x - 2y = 19
answer1. a. (2.2), 3(2, 2), 3 = (x - 2) 2 + (y - 2) 2 = 32= (X - 2) 2 + (y - 2) 2 = 9b. (0.5), 4(0, 5), 4 = (x - 0) 2 + (y - 5) 2 = 42= (X - 0) 2 + (y - 5) 2 = 16
  c. (-5.2), 6(-5, 2), 6 = (x - (-5)) 2 + (y - 2) 2 = 62= (X + 5) 2 + (y - 2) 2 = 36d. (2, -3), 4(2, -3); 4 = (x - 2) 2 + (y - (-3)) 2 = 42= (X - 2) 2 + (y + 3) 2 = 16e. (-4, -3), 5(-4, -3), 5 = (x - (-4)) 2 + (y - (-3)) 2 = 52= (X + 4) 2 + (y + 3) 2 = 25f. (-6.6) 2(-6, 6); 2 = (x - (-6)) 2 + (y - 6) 2 = 22= (X + 6) 2 + (y - 6) 2 = 4
  2. a. (8.6); or2 = (x-h) 2 + (y-k) 2= (O-8) 2 + (o-6) 2= (-8) 2 + (-6) 2= 64 + 36
                         r2 = 100so (x-8) 2 + (y-6) 2 = 100
              b. (-1.1), (3.3)
 r2 = [3 - (-1)] 2 + [3-1] 2= [4] 2 + [2] 2= 16 + 4
            r2 = 20so [x-(-1)] 2 + [y-1] 2 = 20
    c. (-2.0), (4.3)r2 = [4 - (-2)] 2 + [3-0] 2= 62 + 32= 36 + 9
   r2 = 45so [x-(-2)] 2 + [y-0] 2 = 45
   d. (8, -15); Or2 = [O-8] 2 + [O-(-15)] 2= [-8] 2 + [15] 2= 64 + 225
   r2 = 289so [X-8] 2 + [y-(-15)] 2 = 289

       3. a. x2 + y2-2x-6y +6 = 0
     2B 2A = -2 = -6
     A = -1 B = -3
     (-1 - (-3)) = (-1 +3)
r = √ (A ^ 2 + B ^ 2 - C)= √ (〖(-1)〗 ^ 2 + 〖(3)〗 ^ 2-6)= √ (1 +9-6)= √ 4r = 2b. x2 + y2-4x-4y = 0
    2B = 2A = -4-y
   A = -2 B = -2r = √ (A ^ 2 + B ^ 2 - C)
  = √ (〖(-2) ^ 2 + 〖〗 (-2)〗 ^ 2-0)
 = √ (4 +4-0)
  = √ 8 = √ 4. √ 2r = 2 √ 2c. x2 + y2 +6 x = 0
    2A = 6 2B = 0
    A = 3 B = 0r = √ (A ^ 2 + B ^ 2 - C)= √ (3 ^ 2 +0 ^ 2 - 0)= √ 9
 = 3
          


            d. y2 + x2 +4 x +4 y +7 = 0
      2B 2A = 4 = -4A = 2 B = -2r = √ (A ^ 2 + B ^ 2 - C)
  = √ (2 ^ 2 + 〖(-2)〗 ^ 2-7)
 = √ (4 +4- 7)= √ (8-7)r = √ 1 = 1e. x2 + y2 +8 x-2y = 19
   2A = 8 2B = -2
     A = 4 B = -1r = √ (A ^ 2 + B ^ 2 - C)
   = √ (4 ^ 2 + 〖(-1)〗 ^ 2-0)
  = √ (16 +1- 0)r = √ 17