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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. Identify vertex form: Identify the vertex form of the parabola.\newlineThe given equation y=−8x2−5y = -8x^2 - 5 is similar to y=a(x−h)2+ky = a(x - h)^2 + k, where a=−8a = -8, h=0h = 0, and k=−5k = -5.
  2. Calculate p value: Calculate 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. Find focus: Find the focus of the parabola using the vertex (h,k)(h, k) and the value of pp. The focus is at (h,k+p)(h, k + p). Focus = (0,−5−132)(0, -5 - \frac{1}{32}) Focus = (0,−16032−132)(0, -\frac{160}{32} - \frac{1}{32}) Focus = (0,−16132)(0, -\frac{161}{32})

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