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angle asymptotes axes axis base becomes called centre chord circle circumscribing co-ordinates coefficients coincide common tangents condition conic conic section conjugate considered constant corresponding curve denote determine diameter difference distance double 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 obtain origin pair parabola parallel particular pass perpendicular point of contact polar pole position projection properties 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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