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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
133
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C
6
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D
8
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Solution

The correct options are
A 1
B 133
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 putting 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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