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If the points (2,0),(0,1),(4,5)and (0,c)are concyclic, then the value of "c" is ?

If the points (2,0),(0,1),(4,5)and (0,c)are concyclic, then the value of "c" is ?

Grade:12

1 Answers

Aman Bansal
592 Points
9 years ago

Dear Shabuddin,

first find the equation of circle passes through point(2,0) ,(0,1) and (4,5)

equation of the circle

x2 +y2 +2gx +2fy +c =0

so put the points

 4+ 4g +c =0 .............1

 1 +2f +c =0 ..............2

39 + 8g + 10f +c =0 ............3

solve these equation

g =-25/12

f =-8/3

c =13/3

so equation of circle

x2 + y2 -25x/6 -16y/3 +13/3 =0

now point(0,c) satisfy this equation

c2 -16c/3 + 13/3 =0

3c2 -16c +13 =0

c=1 ,13/3

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