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What is the directrix of the parabola y=-7x^(2)? Simplify any fractions.

What is the directrix of the parabola y=−7x2? y=-7 x^{2} ? \newlineSimplify any fractions.

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Full solution

Q. What is the directrix of the parabola y=−7x2? y=-7 x^{2} ? \newlineSimplify any fractions.
  1. Identify 'a' value: Identify the value of 'a' in the equation y=−7x2y = -7x^2.\newlineSince the standard form of a parabola is y=ax2y = ax^2, here a=−7a = -7.
  2. Use directrix formula: Use the formula for the directrix of a parabola, which is y=−14ay = -\frac{1}{4a}, to find the directrix.\newlineSubstitute a=−7a = -7 into the formula to get the directrix.
  3. Calculate directrix: Perform the calculation for the directrix: y=−1/(4∗(−7))y = -1/(4*(-7)).\newlineSimplify the fraction to get y=1/28y = 1/28.

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