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What is the center of the hyperbola 4x2−y2−16=04x^2 - y^2 - 16 = 0?\newline(_,_)(\_,\_)

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Q. What is the center of the hyperbola 4x2−y2−16=04x^2 - y^2 - 16 = 0?\newline(_,_)(\_,\_)
  1. Rewrite Equation: Rewrite the equation to isolate the constant term on one side.\newlineMove the constant term to the right side of the equation.\newline4x2−y2−16=04x^2 - y^2 - 16 = 0 becomes 4x2−y2=164x^2 - y^2 = 16.
  2. Convert to Standard Form: Convert the equation into the standard form of a hyperbola.\newlineDivide both sides of the equation by 1616 to get x24−y216=1\frac{x^2}{4} - \frac{y^2}{16} = 1.
  3. Identify Center: Identify the center of the hyperbola.\newlineThe standard form of a hyperbola 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 of the hyperbola. In our equation x2/4−y2/16=1x^2/4 - y^2/16 = 1, we can see that h=0h = 0 and k=0k = 0, so the center is at (0,0)(0, 0).

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