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What is the center of the ellipse 6x2+y2−36=06x^2 + y^2 - 36 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 6x2+y2−36=06x^2 + y^2 - 36 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide and Simplify: Now, we need to get the equation in standard form for an ellipse. Divide both sides by 3636 to get the coefficients of x2x^2 and y2y^2 to be 11. 6x236+y236=3636\frac{6x^2}{36} + \frac{y^2}{36} = \frac{36}{36} x2/6+y2/36=1x^2/6 + y^2/36 = 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 x2/6+y2/36=1x^2/6 + y^2/36 = 1, which is the same as (x−0)2/6+(y−0)2/36=1(x-0)^2/6 + (y-0)^2/36 = 1.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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