Problem

Select the equations for the directrix lines for the hyperbola defined by the equation \( \frac{x^{2}}{20}-\frac{y^{2}}{10}=1 \)

Answer

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Answer

\(Directrix1: x = \pm\frac{a^2}{c} = \pm\frac{20}{\sqrt{30}}\)

Steps

Step 1 ：\(a^2 = 20, b^2 = 10\)

Step 2 ：\(c = \sqrt{a^2 + b^2} = \sqrt{20 + 10}\)

Step 3 ：\(c = \sqrt{30}\)

Step 4 ：\(Directrix1: x = \pm\frac{a^2}{c} = \pm\frac{20}{\sqrt{30}}\)

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