Q. What is the center of the hyperbola x2−y2=49?(_,_)
Identify Standard Form: Identify the standard form of the hyperbola equation.The standard form of a hyperbola centered at (h,k) is a2(x−h)2−b2(y−k)2=1 for a horizontal hyperbola or b2(y−k)2−a2(x−h)2=1 for a vertical hyperbola. We need to compare the given equation x2−y2=49 with the standard form to find the center.
Rewrite Equation: Rewrite the given equation in standard form.The given equation is x2−y2=49. To compare it with the standard form, we can rewrite it as (x2)/49−(y2)/49=1, which simplifies to (x2)/72−(y2)/72=1.
Identify Center: Identify the center of the hyperbola.From the standard form (72x2−72y2=1, we can see that h=0 and k=0, since there are no terms (x−h) or (y−k) in the equation. Therefore, the center of the hyperbola is at the origin (0,0).
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