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What is the focus of the parabola y=9x2y = 9x^2?\newlineSimplify any fractions.\newline(______,______)

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Q. What is the focus of the parabola y=9x2y = 9x^2?\newlineSimplify any fractions.\newline(______,______)
  1. Identify orientation: Identify the orientation of the parabola.\newlineSince the equation is y=9x2y = 9x^2, it's a vertical parabola.
  2. Write in vertex form: Write the equation in vertex form to find aa, hh, and kk. The equation y=9x2y = 9x^2 is already in the form y=a(x−h)2+ky = a(x - h)^2 + k, where a=9a = 9, h=0h = 0, and k=0k = 0.
  3. Calculate p value: Calculate the value of p using the formula p=14ap = \frac{1}{4a}.p=14×9p = \frac{1}{4\times 9}p=136p = \frac{1}{36}
  4. Find focus: Find the focus of the parabola using the values of hh, kk, and pp.\newlineSince the parabola is vertical, the focus is (h,k+p)(h, k + p).\newlineFocus = (0,0+136)(0, 0 + \frac{1}{36})\newlineFocus = (0,136)(0, \frac{1}{36})

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