If the point (2 ,0 ) , (0 ,1 ) , (4 ,5 ) and ( 0 ,c) are con-cyclic, then integral value of c is equal to

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Accepted Answer

Correct answer: 1. 1JEE Main 2020 Circle with (2 ,0 ) , (0 ,1 ) as end points of diameter is (x-2 )x+ (y-1 )y=0 and line through these two points is y-0= ( -12 ) (x-2 )or 2y+x-2=0 Family of circles through these two points are x (x-2 )+y (y-1 )+ (2y+x-2 )=0 It passes through (4 ,5 ) i.e., 4 (2 )+5 (4 )+ (10+4-2 )=0 ⇒ = -73. Hence equation of circle is x (x-1 )+y (y-1 )- 73 (2y+x-2 )=0 It passes through ( 0 ,c), therefore c (c-1 )- 73 (2c-2 )=0 c (c-1 )- 73 (2c-2 )=0 or c= 143 and 1

$If the point (2, 0), (0, 1), (4, 5) and (0, c) are con-cyclic, then integral value of c is equal to$

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