A circle passes through the point (-1, -3) and its diameter is 20 units.
If the coordinates of its center are (3a + 1, 2a – 1), find the value of a
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By distance formula ,
D = √( 3a + 1 - (-1))² + ( 2a - 1 - (-3))²
20/2 = √( 3a + 2 )² + ( 2a + 2 )²
100 = 9a² + 4 + 12a + 4a² + 4 + 8a
13a² + 20a - 92 = 0
a = ( - 20 ± √ 400 + 4784 ) / 26
a = ( - 20 ± 72 )/ 26
a = 52/26 , -92/26
Distance is always positive so ,
a = 2
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