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What is the center of the hyperbola 25x2−y2−100=025x^2 - y^2 - 100 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola 25x2−y2−100=025x^2 - y^2 - 100 = 0?\newline(_,_)(\_,\_)
  1. Move constant term: 25x2−y2−100=025x^2 - y^2 - 100 = 0\newlineMove the constant term to the right side.\newline25x2−y2=10025x^2 - y^2 = 100
  2. Convert to standard form: 25x2−y2=10025x^2 - y^2 = 100\newlineConvert the equation into standard form.\newlineDivide both sides of the equation by 100100.\newline(25x2)/100−y2/100=100/100(25x^2)/100 - y^2/100 = 100/100\newlinex2/4−y2/100=1x^2/4 - y^2/100 = 1
  3. Find center of hyperbola: x24−y2100=1\frac{x^2}{4} - \frac{y^2}{100} = 1\newlineFind the center of the hyperbola.\newlineThe standard form of the equation of a hyperbola centered at (h,k)(h, k) is (x−h)2a2−(y−k)2b2=1\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\newlineHere, the equation can be written as (x−0)24−(y−0)2100=1\frac{(x - 0)^2}{4} - \frac{(y - 0)^2}{100} = 1.\newlineThus, h=0h = 0 and k=0k = 0.\newlineCenter of the hyperbola: (0,0)(0, 0)

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