Circle
Forma of equations
Tangent
Radical axis
Geometry/applications
Normal
Family of circles
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Different cases of 2 circles
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Circle :
Intersection of circles
one inside another
Touching externally
Touching internally
Disjoint circles
Intersecting
Different forms of equations
Parametric form
x = r cos θ y = r sin θ
Circumscribing polygon
Triangle
L1L2 + $L2L3 + #L3L1 = 0
Quadrilateral
L1L2 + $L3L4 = 0
Two points on circle and chord subtending angle b/w them
Two points of diameter
(x-x1)(x-x2) + (y-y1)(y-y2) = 0
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Coordinate axes
Radius and centre
Tangent
Chord of contact
Equation of pair of tangents
Normal to circle
Eq of tangent drawn to cirlce from external point
Director circle
Equation of tangent to circle having given slope
Geometrical properties
Position of point wrt circle
S1 >, =, < 0
Position of line wrt circle
D >, =, < 0
Equation of Chord of circle
T = S1
Length of tangent to circle
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Secant
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Max/Min dist b/w point and circle
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Family of Circles
Two points
Two intersecting circles
Fixed circle and line
Fixed point and a line
Radical Axis
Orthogonal intersection of circles
Of 3 cirlces
Of 2 circles
Cond for 2 degree homo eqn to represent circle
a=b
h =0
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Intercept of circle on axes
Eqn of circle passing through 3 points
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Equation of tangent to citcle on a point on circle