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Question

Equation of the circle which touches the coordinate axes and passes through the point (2,1) is ?

A
x2+y2+8x+8y29=0
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B
x2+y210x10y+25=0
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C
x2+y2+10x+10y35=0
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D
x2+y220x20y+55=0
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Solution

The correct option is B x2+y210x10y+25=0
Let the required equation be x2+y2+2gx+2fy+c=0
It passes through the point (2,1)
4+1+4g+2f+c=04g+2f+c+5=0(1)
It touches x-axis
g2c=0g2=c(2)
It touches y-axis
f2c=0f2=c(3)
From (2),(3)

g2=f2g=f(4)
Put (2)(4) in (1)
4g+2g+g2+5=0g2+6g+5=0(g+1)(g+5)=0g=1,5
Put g=5f=5c=25
So the required Equation is x2+y210x10y+25=0

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