Question

the centre of circle is (2a-1,3a+1) and it pass through the point (-3,-1)find the value of a if a diameter of circle is 20 units

Answer 1

Diameter of circle =20 units

Radius =10 units

Let C(2a-1 , 3a+1) be the centre and A(-3 , -1) be the point..

Using distance formula,

$10 = \sqrt{ {(2a - 1 + 3)}^{2} + {(3a + 1 + 1)}^{2} } \\ 100 = {(2a + 2)}^{2} + {(3a + 2)}^{2} \\ 100 = 4 {a}^{2} + 4 + 8a + 9 {a}^{2} + 4 \: + 12a \\ 100 = 13 {a}^{2} + 20a + 8 \\ 13 {a}^{2} + 20a - 92 = 0 \\ 13 {a}^{2} - 26a + 46a - 92 = 0 \\ 13a(a - 2) + 46(a - 2) = 0 \\ (13a + 46) = 0 \: \: or \: \: ( a - 2) \\ a = - \frac{46}{13} \: \: or \: \: a = 2$

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Answer 2

Answer:

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