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anharmonic ratio asymptotes axes bisected bisectors Brianchon's theorem centre chord of contact circumscribing coefficients coincide common tangents conic passing conic section conic touching constant ratio cosC denote determine directrix double contact drawn ellipse envelope equal find the equation find the locus fixed line fixed point foci focus four points given conic given line given point Hence homographic hyperbola imaginary points infinite distance inscribed intercept joining the points last Article line at infinity line joining line meets meet the curve middle points origin pair of tangents parabola parallel Pascal's theorem pencil perpendicular plane point of contact point x'y points at infinity points of intersection polar pole projection proved quadrilateral radical axis radius vector reciprocal rectangle represents right angles right line second degree self-conjugate sides sin2 square Steiner's theorem substituting subtended tangential equation theorem three conies transformed trilinear vanish vertex vertices
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