5. (25 points) Two hyperbolas that have the same set of asymptotes are called conjugate. Show that the hyperbolas \[ \frac{x^{2}}{4}-y^{2}=1 \quad \text { and } \quad y^{2}-\frac{x^{2}}{4}=1 \] are conjugate. Graph each parabola on the same set of coordinate axis.
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The asymptotes of the hyperbola are given by the lines y = ±b/a * x. Show more…
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Two hyperbolas that have the same set of asymptotes are called conjugate. Show that the hyperbolas $$ \frac{x^{2}}{4}-y^{2}=1 \quad \text { and } \quad y^{2}-\frac{x^{2}}{4}=1 $$ are conjugate. Graph each hyperbola on the same set of coordinate axes.
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