Question

Q14 Find equation of directrix of parabola 2x^(2) =-y




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Answer 1

Given equation :-

• -y = 2x²

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To find :-

• Directrix of the parabola.

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Solution :-

• The eqn. of the directrix of the parabola is given by

→ x² = 4ay

• a + y = 0⠀⠀.... [1]

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From the given equation

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→ $\sf{-y = 2x^2}$

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→ $\sf{x^2 = \dfrac{-y}{2}}$

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Putting the value of x² in the standard equation of the directrix.

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→ $\sf{\dfrac{-y}{2} = 4ay}$

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→ $\sf{\dfrac{-1}{2} = 4a}$

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→ $\sf{a = \dfrac{-1}{8}}$

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Substituting the value of a in [1]

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$\tt\longrightarrow{\dfrac{-1}{8} + y = 0}$

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$\tt\longrightarrow{\dfrac{-1 + 8y}{8} = 0}$

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$\tt\longrightarrow{-1 + 8y = 0}$

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$\tt\longrightarrow{8y - 1 = 0}$

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Hence, the required equation of the directrix is 8y - 1 = 0.