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