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What is the focus of the parabola y=7x2−2y = 7x^2 - 2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=7x2−2y = 7x^2 - 2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify Parabola Form: y=7x2−2y = 7x^2 - 2 is a vertical parabola, so it's in the form y=a(x−h)2+ky = a(x - h)^2 + k.
  2. Find aa, hh, kk: Identify aa, hh, and kk. Here, a=7a = 7, h=0h = 0, and k=−2k = -2.
  3. Calculate pp: Find the value of pp using p=14ap = \frac{1}{4a}. So, p=14×7p = \frac{1}{4 \times 7}.
  4. Determine Focus: Calculate pp. p=128p = \frac{1}{28}.
  5. Simplify k+pk + p: The focus of a vertical parabola is (h,k+p)(h, k + p). So, the focus is (0,−2+128)(0, -2 + \frac{1}{28}).
  6. Final Focus: Simplify k+pk + p. −2+128=−5528-2 + \frac{1}{28} = -\frac{55}{28}.
  7. Final Focus: Simplify k+pk + p. −2+128=−5528-2 + \frac{1}{28} = -\frac{55}{28}.The focus of the parabola is (0,−5528)(0, -\frac{55}{28}).

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