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What is the center of the ellipse 9x2+2y2−18=09x^2 + 2y^2 - 18 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 9x2+2y2−18=09x^2 + 2y^2 - 18 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide by 1818: Now, divide the entire equation by 1818 to get the standard form of the ellipse equation.\newline(9x2)/18+(2y2)/18=18/18(9x^2)/18 + (2y^2)/18 = 18/18\newlineThis simplifies to x2/2+y2/9=1x^2/2 + y^2/9 = 1
  2. Standard form of ellipse: The standard form of an ellipse is (x−h)2/a2+(y−k)2/b2=1(x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k)(h, k) is the center.\newlineHere, we have x2/2+y2/9=1x^2/2 + y^2/9 = 1, which can be written as (x−0)2/2+(y−0)2/9=1(x-0)^2/2 + (y-0)^2/9 = 1.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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