The centre of a circle is (2α - 1, 7) and it passes through the point (- 3, - 1). If the diameter of the circle is 20 units, then find the value(s) of α.

Let co-ordinates of centre be 0(2α - 1,7), which passes through the point A(- 3, - 1).

Fig. 7.23(A)
Now OA = 10 units

$OA space equals space square root of left parenthesis 2 straight alpha minus 1 plus 3 right parenthesis squared plus left parenthesis 7 plus 1 right parenthesis squared end root 10 space equals space square root of 4 straight a squared plus 4 plus 8 straight alpha plus 64 end root$

Squaring
100 = 4α² + 8α + 68
4α² + 8α - 32 = 0
α² + 2α - 8 = 0
α² + 4α + 2α - 8 = 0
α(α + 4) + 2(α - 8) = 0
(α - 4) (α - 2) = 0
α = -4, α = 2.

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