Question:
the centre of a circle is [2a-1,3a+1]. find 'a' if the circle passes through [-3,-1] and the length of its diameter is 20 units.
Answer:
Let the center of the circle is O(2a + 1, 3a + 1)
Given length of the diameter = 20
So, radius = 20/2 = 10
Since the circle passes through point P(-3, -1)
So, OP = 10
=> OP2 = 100
=> (2a - 1 + 3)2 + (3a + 1 + 1)2 = 100
=> (2a + 2)2 + (3a + 2)2 = 100
=> 4(a + 1)2 + (3a + 2)2 = 100
=> 4(a2 + 2x + 1) + 9a2 + 4 + 12x = 100
=> 4a2 + 8a + 4 + 9a2 + 4 + 12a = 100
=> 13a2 + 20a + 8 = 100
=> 13a2 + 20a + 8 - 100 = 0
=> 13a2 + 20a - 92 = 0
=> (13a + 46)*(a - 2) = 0
=> a = 2, -46/13
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