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