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What is the center of the hyperbola 16x2−y2−64=016x^2 - y^2 - 64 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola 16x2−y2−64=016x^2 - y^2 - 64 = 0?\newline(_,_)(\_,\_)
  1. Move constant term: 16x2−y2−64=016x^2 - y^2 - 64 = 0\newlineMove the constant term to the right side of the equation.\newline16x2−y2=6416x^2 - y^2 = 64
  2. Convert to standard form: 16x2−y2=6416x^2 - y^2 = 64\newlineConvert the equation into standard form by dividing both sides by 6464.\newline(16x2)/64−(y2)/64=64/64(16x^2)/64 - (y^2)/64 = 64/64\newlinex2/4−y2/64=1x^2/4 - y^2/64 = 1
  3. Identify center: x24−y264=1\frac{x^2}{4} - \frac{y^2}{64} = 1\newlineIdentify the center of the hyperbola.\newlineThe equation can be written as (x−0)2/4−(y−0)2/64=1(x - 0)^2/4 - (y - 0)^2/64 = 1.\newlineHere h=0h = 0 and k=0k = 0.\newlineCenter of the hyperbola: (0,0)(0, 0)

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