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Question
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
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Solution
Distance between the points A (2x - 1, 3x + 1) and B (- 3, - 1) = Radius of circle
AB = 10 (Since, diameter = 20 units, given)
AB2 = 100
(-3 - 2x + 1)2 + (-1 - 3x - 1)2 = 100
(-2 - 2x)2 + (-2 - 3x)2 = 100
4 + 4x2 + 8x + 4 + 9x2 + 12x = 100
13x2 + 20x - 92 = 0
x = `(-20 ± sqrt(400 + 4784))/(26)`
x = `(-20 ± 72)/(26)`
x = 2, - `(46)/(13)`.
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
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Using the picture of a hockey field below, answer the questions that follow:
The coordinates of the centroid of ΔEHJ are ______.
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