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Conic sections

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Horizontal hyperbola and translation

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Two panels: x²/a²−y²/b²=1 has centre(0,0), vertices (±a,0), symmetry x=0,y=0 and asymptotes y=±(b/a)x. Translation by h,k gives centre(h,k), vertices (h±a,k), symmetry x=h,y=k and asymptotes y=k±(b/a)(x−h). Source illustration assumes h>0,k>0; figures explicitly use a=2,b=1,h=4,k=2.
Two panels: x²/a²−y²/b²=1 has centre(0,0), vertices (±a,0), symmetry x=0,y=0 and asymptotes y=±(b/a)x. Translation by h,k gives centre(h,k), vertices (h±a,k), symmetry x=h,y=k and asymptotes y=k±(b/a)(x−h). Source illustration assumes h>0,k>0; figures explicitly use a=2,b=1,h=4,k=2.
Two panels: x²/a²−y²/b²=1 has centre(0,0), vertices (±a,0), symmetry x=0,y=0 and asymptotes y=±(b/a)x. Translation by h,k gives centre(h,k), vertices (h±a,k), symmetry x=h,y=k and asymptotes y=k±(b/a)(x−h). Source illustration assumes h>0,k>0; figures explicitly use a=2,b=1,h=4,k=2.
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