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Question

Find the equation of radical axis of two circle x2 + y2 − 4x − 2y = 4 and x2 + y2 − 12x − 8y = 12.


A

4x + 3y + 4 = 0

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B

4x 3y 4 = 0

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C

4x 3y + 4 = 0

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D

3x + 4y 4 = 0

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Solution

The correct option is A

4x + 3y + 4 = 0


Radical axis of two circles is the locus of points whose powers with respect to the two circles are equal.
OR
we can say it is the locus of points at which tangents drawn to both circles have the same length.
Equation of radical axis of the two circles S1 = 0 & S2 = 0 is given by

S1 S2 = 0

Here, S1 is x2 + y2 4x 2y 4 = 0

S2 is x2 + y2 12x 8y 12 = 0

Equation of the radical axis is

S1 S2 = 0

x2 + y2 4x 2y 4 (x2 + y2 12x 8y 12) = 0

x2 + y2 4x 2y 4 x2 y2 + 12x + 8y + 12 = 0

8x + 6y + 8 = 0

4x + 3y + 4 = 0

Equation of radical axis is 4x + 3y + 4 = 0

Option A is correct


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