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Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.
Welcome to AskIItiansGiven that: Foci (0, ±13), Conjugate axis length = 24It is noted that the foci are on the y-axis.Therefore, the equation of the hyperbola is of the form:(y^2/a^2)-(x^2/b^2) = 1 …(1)Since the foci are (0, ±13), we can getC = 13It is given that, the length of the conjugate axis is 24,It becomes 2b = 24b= 24/2b= 12And, we know that a^2+ b^2= c2To find a, substitute the value of b and c in the above equation:a^2+ 122= 132a^2= 169-144a^2= 25Now, substitute the value of a and b in equation (1), we get(y^2/25)-(x^2/144) = 1, which is the required equation of the hyperbola.Thanks
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