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What is the focus of the parabola y=−x2y= -x^2? \newlineSimplify any fractions.

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Full solution

Q. What is the focus of the parabola y=−x2y= -x^2? \newlineSimplify any fractions.
  1. Identify 'a' value: We are given the equation of the parabola: y=−x2y = -x^2. To find the focus, we need to identify the value of 'a' in the standard form of a parabola y=ax2y = ax^2. Here, a=−1a = -1.
  2. Standard form of parabola: The standard form of a parabola with its vertex at the origin (0,0)(0,0) and axis of symmetry along the y-axis is y=ax2y = ax^2. The focus of such a parabola is given by the point (0,14a)(0, \frac{1}{4a}).
  3. Substitute 'a' value: Substitute a=−1a = -1 into the formula for the focus (0,14a)(0, \frac{1}{4a}).\newlineFocus of the parabola: (0,14×(−1))(0, \frac{1}{4 \times (-1)}).
  4. Calculate focus: Calculate the value of 14×(–1)\frac{1}{4 \times (–1)}.\newlineFocus of the parabola: (0,–14)(0, –\frac{1}{4}).

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