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What is the focus of the parabola y=−10x2y = -10x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=−10x2y = -10x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify Orientation: Identify the orientation of the parabola. Since the equation is y=−10x2y = -10x^2, it's a vertical parabola.
  2. Find Values: Find the values of aa, hh, and kk from the equation y=−10x2y = -10x^2.\newlineComparing with y=a(x−h)2+ky = a(x - h)^2 + k, we get a=−10a = -10, h=0h = 0, and k=0k = 0.
  3. Calculate pp: Calculate the value of pp using the formula p=14ap = \frac{1}{4a}.p=14(−10)=−140p = \frac{1}{4(-10)} = -\frac{1}{40}.
  4. Determine Focus: Determine the focus of the parabola using the values of hh, kk, and pp. The focus is at (h,k+p)(h, k + p), so it's (0,0−140)(0, 0 - \frac{1}{40}) which simplifies to (0,−140)(0, -\frac{1}{40}).

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