Question

Part 6: Use the information provided to write the standard form equation of each circle

16. Ends of a diameter: (-5, 5) and (-5, 7)

17. Ends of a diameter: (2, -9) and (10, -9)

18. Ends of a diameter: (-9, 14) and (-9, -8)

Answer 1

16. (x + 5)² + (y - 6)² = 1

17. (x - 6)² + (y + 9)² = 16

18. (x + 9)² + (y - 3)² = 121

Explanation:

Circle:

(x - h)² + (y - k)² = r²

16. Ends of a diameter: (-5, 5) and (-5, 7)

(h,k) = (-5-5)/2, (5+7)/2 = (-5,6)

Diameter = 7 - 5 = 2

Radius = 2/2 = 1

(x - (-5))² + (y - 6)² = 1²

(x + 5)² + (y - 6)² = 1

17. Ends of a diameter: (2, -9) and (10, -9)

(h,k) = (2+10)/2,(-9-9)/2 = (6,-9)

Diameter = 10 - 2 = 8

Radius = 8/2 = 4

(x - 6)² + (y - (-9))² = 4²

(x - 6)² + (y + 9)² = 16

18. Ends of a diameter: (-9, 14) and (-9, -8)

(h,k) = (-9-9)/2, (14-8)/2 = (-9,3)

Diameter = 14 - (-8) = 22

Radius = 22/2 = 11

(x - (-9))² + (y - 3)² = 11²

(x + 9)² + (y - 3)² = 121

Answer 2

16. (x+5)² + (y-6)² = 1

17. (x-6)² + (y+9)² = 16

18. (x+9)² + (y-3)² = 121

Explanation:

Please see the attached pictures for full solution.