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

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Q. What is the center of the hyperbola x2−y2=4x^2 - y^2 = 4?\newline(_,_)(\_,\_)
  1. Write Standard Form: We start by writing the given equation of the hyperbola in standard form.\newlineThe given equation is x2−y2=4x^2 - y^2 = 4.\newlineTo get it into standard form, we want it to look like (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.
  2. Compare to Standard Form: Since the equation is already set equal to a constant, we can compare it directly to the standard form.\newlineThe given equation x2−y2=4x^2 - y^2 = 4 can be rewritten as x24−y24=1\frac{x^2}{4} - \frac{y^2}{4} = 1.
  3. Identify Center: Now, we can see that the equation is in the form (x−0)2/4−(y−0)2/4=1(x - 0)^2/4 - (y - 0)^2/4 = 1. This means that h=0h = 0 and k=0k = 0, so the center of the hyperbola is at the origin (0,0)(0, 0).

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