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What is the focus of the parabola y=−8x2+5y = -8x^2 + 5?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−8x2+5y = -8x^2 + 5?\newlineSimplify any fractions.\newline(______,______)
  1. Write Equation in Vertex Form: Write the equation in vertex form.\newliney=−8(x−0)2+5y = -8(x - 0)^2 + 5\newlineHere, a=−8a = -8, h=0h = 0, and k=5k = 5.
  2. Find Value of p: Find the value of pp using the formula p=14ap = \frac{1}{4a}.p=14(−8)p = \frac{1}{4(-8)}p=−132p = -\frac{1}{32}
  3. Determine Focus: Determine the focus of the parabola using the vertex (h,k)(h, k) and the value of pp.\newlineFocus = (h,k+p)(h, k + p)\newlineFocus = (0,5−132)(0, 5 - \frac{1}{32})
  4. Simplify Coordinates: Simplify the coordinates of the focus.\newlineFocus = (0,16032−132)(0, \frac{160}{32} - \frac{1}{32})\newlineFocus = (0,15932)(0, \frac{159}{32})

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