Question

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

Answer 1

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