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What is the focus of the parabola y=−7x2−5y = -7x^2 - 5?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−7x2−5y = -7x^2 - 5?\newlineSimplify any fractions.\newline(______,______)
  1. Vertical Parabola: y=−7x2−5y = -7x^2 - 5 is a vertical parabola.
  2. Identify Parameters: Identify aa, hh, and kk from y=a(x−h)2+ky = a(x - h)^2 + k.\newliney=−7(x−0)2−5y = -7(x - 0)^2 - 5 gives a=−7a = -7, h=0h = 0, k=−5k = -5.
  3. Calculate pp: Find the value of pp using p=14ap = \frac{1}{4a}.p=14(−7)=−128p = \frac{1}{4(-7)} = -\frac{1}{28}.
  4. Find Focus: The focus of a vertical parabola is (h,k+p)(h, k + p). Substitute h=0h = 0, k=−5k = -5, and p=−128p = -\frac{1}{28}. Focus: (0,−5−128)(0, -5 - \frac{1}{28}).
  5. Simplify Focus: Simplify −5−128-5 - \frac{1}{28}.\newlineFocus: (0,−14028−128)=(0,−14128)(0, -\frac{140}{28} - \frac{1}{28}) = (0, -\frac{141}{28}).

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