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What is the center of the ellipse 15x2+2y2−30=015x^2 + 2y^2 - 30 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 15x2+2y2−30=015x^2 + 2y^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(15x230)+(2y230)=3030(\frac{15x^2}{30}) + (\frac{2y^2}{30}) = \frac{30}{30}\newlinex22+y215=1\frac{x^2}{2} + \frac{y^2}{15} = 1
  2. Standard Form Equation: 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+y2/15=1x^2/2 + y^2/15 = 1, which can be written as (x−0)2/2+(y−0)2/15=1(x-0)^2/2 + (y-0)^2/15 = 1.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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