thr centre of a circle is ( 2a-1 , 3a+ 1) anf it passes through the point (2,3). Find the values of 'a' if a diameter of the circle is og length 20 units
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we know,
radius is the distance between centre to a point lies on circumference of circle .
also radius = diameter/2
so, radius = 10 unit .
now,
according to above explanation radius equal to distance between (2a -1, 3a +1 ) and (2 , 3)
use,distance formula of co-ordinate geometry
radius = √{( 2a -1 -2)² + (3a + 1 -3)² }
10 = √{(2a -3)² + (3a -2)² }
take square both sides,
100 = (2a -3)² + (3a -2)²
100 = 4a² -12a + 9 +9a² -12a + 4
100 = 13a² -24a + 13
13a² -24a -87 = 0
a = { 24 ± √24² + 4×87×13)}/26
= { 24 ±√(576 + 4524)}/26
= {24 ± 10√51}/26
radius is the distance between centre to a point lies on circumference of circle .
also radius = diameter/2
so, radius = 10 unit .
now,
according to above explanation radius equal to distance between (2a -1, 3a +1 ) and (2 , 3)
use,distance formula of co-ordinate geometry
radius = √{( 2a -1 -2)² + (3a + 1 -3)² }
10 = √{(2a -3)² + (3a -2)² }
take square both sides,
100 = (2a -3)² + (3a -2)²
100 = 4a² -12a + 9 +9a² -12a + 4
100 = 13a² -24a + 13
13a² -24a -87 = 0
a = { 24 ± √24² + 4×87×13)}/26
= { 24 ±√(576 + 4524)}/26
= {24 ± 10√51}/26
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