What are the foci of the hyperbola represented by the equation (x^(2))/(5)-(y^(2))/(7)=1? Choose 1 answer: (A) (0,sqrt12) and (0,-sqrt12) (B) (sqrt12,0) and (-sqrt12,0) (c) (sqrt74,0) and (-sqrt74,0) (D) (0,sqrt74) and (0,-sqrt74)

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What are the foci of the hyperbola represented by the equation  (x^(2))/(5)-(y^(2))/(7)=1? Choose 1 answer: (A)  (0,sqrt12) and  (0,-sqrt12) (B)  (sqrt12,0) and  (-sqrt12,0) (c)  (sqrt74,0) and  (-sqrt74,0) (D)  (0,sqrt74) and  (0,-sqrt74)

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Equation form of hyperbola: The given equation is in the form of a hyperbola with the equation (x^2)/(a^2) - (y^2)/(b^2) = 1, where a^2 is under the x^2 term and b^2 is under the y^2 term. For a hyperbola of this form, the foci are located at (±c, 0) if the x^2 term is positive, and at (0, ±c) if the y^2 term is positive, where c is the distance from the center to each focus.Identifying a^2 and b^2: We identify a^2 and b^2 from the given equation. Here, a^2 = 5 and b^2 = 7. The next step is to find the value of c, which is calculated using the formula c^2 = a^2 + b^2 for hyperbolas.Calculating the value of c: We calculate c^2 using the values of a^2 and b^2: c^2 = 5 + 7 = 12. Therefore, c = sqrt(12).Locating the foci: Since the x^2 term is positive and comes first in the equation, the foci are located along the x-axis. Thus, the coordinates of the foci are (±sqrt(12), 0).Matching the result with choices: We match our result with the given choices. The correct choice is (B) (sqrt(12),0) and (-sqrt(12),0).

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