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What is the focus of the parabola y=6x2+3y = 6x^2 + 3?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=6x2+3y = 6x^2 + 3?\newlineSimplify any fractions.\newline(______,______)
  1. Identify Vertex Form: Identify the vertex form of the parabola.\newlineThe given equation y=6x2+3y = 6x^2 + 3 is already in the form y=a(x−h)2+ky = a(x - h)^2 + k, where a=6a = 6, h=0h = 0, and k=3k = 3.
  2. Calculate p Value: Calculate the value of p using the formula p=14ap = \frac{1}{4a}.p=14×6p = \frac{1}{4\times 6}p=124p = \frac{1}{24}
  3. Determine Focus: Determine the focus of the parabola.\newlineThe focus is at (h,k+p)(h, k + p) since the parabola opens upwards.\newlineFocus =(0,3+124)= (0, 3 + \frac{1}{24})\newlineFocus =(0,3+0.0416667)= (0, 3 + 0.0416667)
  4. Simplify Focus Coordinates: Simplify the focus coordinates.\newlineFocus = (0,3.0416667)(0, 3.0416667)\newlineSince we need to simplify any fractions, we'll keep the fraction form for the y-coordinate.\newlineFocus = (0,7324)(0, \frac{73}{24})

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