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Question

The locus of the point from which the length of the tangent to the circle x2+y22x4y+4=0 is 3 units is

A
x2+y22x4y9=0
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B
x2+y22x4y4=0
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C
x2+y22x4y3=0
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D
x2+y22x4y5=0
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Solution

The correct option is A x2+y22x4y5=0
Let the point is (h,k).
Then the length of the tangent to the circle x2+y22x4y+4=0 is h2+k22h4k+4 units.
Now according to the given problem we've,
h2+k22h4k+4=3
or, h2+k22h4k+4=9
or, h2+k22h4k5=0.
So the locus of (h,k) is x2+y22x4y9=0.

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