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anharmonic ratio asymptotes axes bisected bisectors chord joining chord of contact chords of intersection circumscribing coefficients coincide common tangents condition conic section conies conjugate diameters corresponding cos0 cosC denote directrix double contact drawn ellipse envelope equa equal express find the co-ordinates find the equation find the locus fixed line fixed point foci focus four points given circles given line given point harmonic Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets line passing meet the curve middle points ordinates origin parabola parallel Pascal's theorem pencil perpendicular point of contact point x'y points at infinity points of intersection polar equation pole proved quadratic quadrilateral radical axis radius vector reciprocal rectangle right angles right line second degree sides square substituting subtended theorem tion touch transform values vertex vertices
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