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Exercise 7.3 · Q75

Q.Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x2−3y2=3x^2 - 3y^2 = 3.

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x2−3y2=3⇒x23−y21=1x^2-3y^2=3 \Rightarrow \dfrac{x^2}{3}-\dfrac{y^2}{1}=1, so a2=3, b2=1a^2=3,\,b^2=1.

Its conjugate hyperbola is y21−x23=1\dfrac{y^2}{1}-\dfrac{x^2}{3}=1, whose own semi-transverse-axis-squared is 11 (the old b2b^2) and semi-conjugate-axis- …

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