A circle has equation x 2 + 2x + y 2 24y 24 = 0

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A circle has equation x2 + 2x + y2 − 24y − 24 = 0

a. Find the centre and radius of the circle.

b. The points A(−13, 17) and B(11, 7) both lie on the circumference of the circle. Show that AB is a diameter of the circle.

c. The point C lies on the negative x-axis and the angle ACB = 90°. Find the coordinates of C.

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