What is radical axis?
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heymate
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Radical Axis
This radical axis of two circles is the locus of a point from which the tangent segments to the two circles are of equal lengths.
Equation of the Radical Axis
In general S – S’ = 0 represents the equation of the Radical Axis to the two circles
i.e. 2x(g – g’) + 2y(f – f’) + c – c’ = 0
where S ≡ x2 + y2 + 2gx + 2fy + c = 0
and S’ ≡ x2 + y2 + 2g’x + 2f’y + c’ = 0
(i) If S = 0 and S’ = 0 intersect in real and distinct points then S – S’ = 0 is the equation of the common chord of the two circles.
(ii) If S’ = 0 and S = 0 touch each other, then S – S’ = 0 is the equation of the common tangent to the two circles at the point of contact.
___________________________
Radical Axis
This radical axis of two circles is the locus of a point from which the tangent segments to the two circles are of equal lengths.
Equation of the Radical Axis
In general S – S’ = 0 represents the equation of the Radical Axis to the two circles
i.e. 2x(g – g’) + 2y(f – f’) + c – c’ = 0
where S ≡ x2 + y2 + 2gx + 2fy + c = 0
and S’ ≡ x2 + y2 + 2g’x + 2f’y + c’ = 0
(i) If S = 0 and S’ = 0 intersect in real and distinct points then S – S’ = 0 is the equation of the common chord of the two circles.
(ii) If S’ = 0 and S = 0 touch each other, then S – S’ = 0 is the equation of the common tangent to the two circles at the point of contact.
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