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What is the center of the ellipse 10x2+3y2−30=010x^2 + 3y^2 - 30 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 10x2+3y2−30=010x^2 + 3y^2 - 30 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide by 3030: Now, divide the entire equation by 3030 to get the standard form of the ellipse equation.\newline(10x2)/30+(3y2)/30=30/30(10x^2)/30 + (3y^2)/30 = 30/30\newlinex2/3+y2/10=1x^2/3 + y^2/10 = 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 x2/3+y2/10=1x^2/3 + y^2/10 = 1, which can be written as (x−0)2/3+(y−0)2/10=1(x-0)^2/3 + (y-0)^2/10 = 1.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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