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Question

If the straight line y = mx + c touches the circle x2+y24y=0, then the value of c will be

A
1+1+m2
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B
1m2+1
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C
2(1+1+m2)
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D
2+1+m2
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Solution

The correct option is C 2(1+1+m2)
Apply for tangency of line, centre being (0, 2) and radius = 2
2+c1+m2=2c24c+4=4+4m2

c=4±16+16m22 or c=2±21+m2
Most correct answer is c=2(1+1+m2).

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