EQUATION OF A CIRCLE WITH END POINTS OF DIAMETER

Problem 1 :

Ends of a diameter : (-9, 5) and (1, 1)

Solution

Problem 2 :

Ends of a diameter : (6, 8) and (16, 6)

Solution

Problem 3 :

Ends of a diameter : (19, 5) and (-5, 1)

Solution

Problem 4 :

Ends of a diameter : (11, -5) and (11, -7)

Solution

Problem 5 :

Given a circle with (5, 1) and (3, -1) as the endpoints of the diameter.

Solution

Problem 6 :

Given a circle with (2, 1) and (6, -3) as the endpoints of the diameter.

Solution

Problem 7 :

Given a circle with (4, -3) and (2, 1) as the endpoints of the diameter.

Solution

Answer Key

1)  x2 + y2 + 8x - 6y - 4 = 0

2)  x2 + y2 - 22x - 14y + 144 = 0

3)  x2 + y2 - 14x - 6y - 90 = 0

4)  x2 - 22x + 156 + y2  + 12y = 0

5)  x2 + y2 - 8x + 14 = 0

6)  x2 + y2 - 8x + 2y + 9 = 0

7)  x2 + y2 - 6x + 2y + 5 = 0

Problem 1 :

A is the point (−3, 1) and B(5, 3).

Find the equation of the circle which has AB as a diameter.

Solution

Problem 2 :

A is the point (-4, 2) and B is (6, -4). Find the equation of the circle which has AB as a diameter.

Solution

Problem 3 :

P is the point (-5, 3) and Q is (5, -21). Find the equation of the circle which has PQ as diameter.

Solution

Answer Key

1)  x2 + y2 - 2x - 4y - 12 = 0

2)  x2 + y2 - 2x + 2y - 32 = 0

3)  x2 + y2 + 18y - 88 = 0

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