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Question

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

A
1
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B
143
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C
5
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D
None of these
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Solution

The correct option is A 1
first, we need to find the equation of circle passes through the point(2,0),(0,1),(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=2512

f=83

c=133

so equation of circle

x2+y225x616y3+133=0

now point(0,c) satisfy this equation

c216c3+133=0

3c216c+13=0

c=1,133

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