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angle asymptotes axes axis base becomes called centre chord circle circumscribing coefficients coincide common tangents condition conic conic section conjugate considered constant coordinates corresponding curve denote determine diameter difference directrix distance drawn ellipse envelope equal equation evidently example express extremities figure find the locus fixed line fixed point focus follows four points give given given point harmonic Hence hyperbola imaginary infinite infinity inscribed intercept intersection length line joining locus manner meet method normal obtain origin pair parabola parallel particular pass pencil perpendicular plane point of contact polar pole position projection proved quantity radical radius ratio reciprocal reduced regard relation represents respect result right line roots satisfied second degree sides square substituting suppose tangents theorem touch transform triangle values vanish vertex vertices write written
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