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What is the center of the ellipse 5x2+2y2−70=05x^2 + 2y^2 - 70 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

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Q. What is the center of the ellipse 5x2+2y2−70=05x^2 + 2y^2 - 70 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Rewrite equation in standard form: Now, we need to rewrite the equation in standard form for an ellipse. Divide both sides by 7070 to get the equation in the form (x2a2)+(y2b2)=1(\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) = 1. (x214)+(y235)=1(\frac{x^2}{14}) + (\frac{y^2}{35}) = 1
  2. Identify center of ellipse: Identify the center of the ellipse from the standard form.\newlineThe standard form 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 (x−h)(x - h) or (y−k)(y - k) terms, hh and kk are both 00.\newlineCenter of the ellipse: (0,0)(0, 0)

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