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What is the center of the ellipse 6x2+13y2−78=06x^2 + 13y^2 - 78 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 6x2+13y2−78=06x^2 + 13y^2 - 78 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide by 7878: Divide the entire equation by 7878 to get the coefficients of x2x^2 and y2y^2 to be 11. \newlinex2(78/6)+y2(78/13)=7878\frac{x^2}{(78/6)} + \frac{y^2}{(78/13)} = \frac{78}{78}\newlineSimplify the fractions.\newlinex213+y26=1\frac{x^2}{13} + \frac{y^2}{6} = 1
  2. Identify center: Identify the center of the ellipse by comparing the equation to the standard form (x−h)2/a2+(y−k)2/b2=1(x-h)^2/a^2 + (y-k)^2/b^2 = 1. The center (h,k)(h,k) is at the origin (0,0)(0,0) since there are no terms to shift the ellipse left/right or up/down.

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