Q. What is the center of the hyperbola 4x2−y2−100=0?(_,_)
Rewrite equation in standard form: Rewrite the equation of the hyperbola in standard form.The given equation is 4x2−y2−100=0. To find the center, we need to express the equation in the standard form of a hyperbola, which is a2(x−h)2−b2(y−k)2=1 for a horizontal hyperbola or a2(y−k)2−b2(x−h)2=1 for a vertical hyperbola, where (h,k) is the center of the hyperbola.First, we move the constant term to the right side of the equation:4x2−y2=100
Move constant term to right side: Divide the equation by the constant term on the right to get 1 on the right side.Divide both sides of the equation by 100 to get the equation in the form of a2x2−b2y2=1:1004x2−100y2=100100Simplify the fractions:25x2−100y2=1
Divide equation by constant term: Identify the center of the hyperbola.The equation 25x2−100y2=1 is now in standard form. The center (h,k) of the hyperbola is the point (0,0) because there are no terms to shift the hyperbola left/right or up/down from the origin.
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