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

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Q. What is the focus of the parabola y=x2y = x^2?\newlineSimplify any fractions.\newline(_,_(\_,\_)\newline
  1. Vertical Parabola: y=x2y = x^2 is a vertical parabola, so it opens upwards.
  2. Standard Form: The standard form of a parabola is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex.
  3. Calculate Parameters: For y=x2y = x^2, a=1a = 1, h=0h = 0, and k=0k = 0, since it's already in the form y=(x−0)2+0y = (x - 0)^2 + 0.
  4. Focus Calculation: The focus of a parabola is (h,k+p)(h, k + p), where p=14ap = \frac{1}{4a}.
  5. Calculate pp: Calculate pp: p=14×1=14p = \frac{1}{4\times 1} = \frac{1}{4}.
  6. Substitute Values: Substitute h=0h = 0, k=0k = 0, and p=14p = \frac{1}{4} into the focus formula: Focus = (0,0+14)(0, 0 + \frac{1}{4}).
  7. Focus of Parabola: The focus of the parabola y=x2y = x^2 is (0,14)(0, \frac{1}{4}).

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