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What is the center of the ellipse 9x2+5y2−90=09x^2 + 5y^2 - 90 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Find properties of ellipses from equations in general formright chevron icon

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Q. What is the center of the ellipse 9x2+5y2−90=09x^2 + 5y^2 - 90 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide by 9090: Now, divide the entire equation by 9090 to get the standard form of the ellipse equation. x210+y218=1\frac{x^2}{10} + \frac{y^2}{18} = 1
  2. Standard Form: 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 x2/10+y2/18=1x^2/10 + y^2/18 = 1, which can be written as (x−0)2/10+(y−0)2/18=1(x-0)^2/10 + (y-0)^2/18 = 1.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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