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III. Determine the center and radius of the circle (10pts)
Center
Radius
No.
Equation
1
x + y2 = 169
2.
(x - 2)² + (y - 4) = 36
ندا
x? + (y - 6) = 25
4
(x + 9)² + y² = 81
5
x² + y² -8x +2y-32 = 0​


Sagot :

SOLUTION

1. x²+y² = 169

  • (x-0)²+(y-0)²=13²
  • Center (0,0) , radius = 13

2. (x-2)² + (y-4)² = 36

  • (x-(2)²+ (y -(4))² = 6²
  • Center (2,4) , radius = 6

3. x²+(y-6)² = 25

  • (x-0)²+(y-6)² = 5²
  • Center (0,6) , radius = 5

4. (x+9)²+y² = 81

  • (x-(-9))²+(y-0)²=9²
  • Center (-9,0) , radius = 9

5. x²+y²-8x+2y-32=0

  • (x²-8x+_)+(y²+2y+_)=32+_+_
  • (x²-8x+16)+(y²+2y+1)=32+16+1
  • (x-4)²+(y+1)²=49
  • (x-4)²+(y-(-1))²=7²
  • Center (4,-1) , radius = 7

ANSWER

  1. Center (0,0) , radius = 13
  2. Center (2,4) , radius = 6
  3. Center (0,6) , radius = 5
  4. Center (-9,0) , radius = 9
  5. Center (4,-1) , radius = 7

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