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What is the center of the ellipse 8x2+y2−64=08x^2 + y^2 - 64 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 8x2+y2−64=08x^2 + y^2 - 64 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Get Equation in Standard Form: Now, we need to get the equation in standard form for an ellipse. Divide both sides by 6464 to get the equation in the form (x2a2)+(y2b2)=1(\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) = 1. x28+y264=1\frac{x^2}{8} + \frac{y^2}{64} = 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.\newlineSince there are no hh and kk in our equation, it means h=0h=0 and k=0k=0.\newlineSo, the center of the ellipse is (0,0)(0, 0).

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