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If the lengths of the transverse axis and the latusrectum of a hyperbola are 6 and `(8)/(3)` respectively, then the equation of the hyperbola is . . .A. `4x^(2)-9y^(2)=72`B. `4x^(2)-9y^(2)=36`C. `9x^(2)-4y^(2)=72`D. `9x^(2)-4y^(2)=36` |
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Answer» Correct Answer - B We have, Length of transverse axis 2a = 6`!`a = 3 and length of latusrectum ,`(2b^(2))/a=8/3` `!2b^(2)=8/3xx3=8!b^(2)=4` `therefore ` Required fo hyperhbola is `(x^(2))/(a^(2)) -(y^(2))/(b^(2)) = 1 rArr (x^(2))/(9) - (y^(2))/(4) = 1 rArrr 4x^(2) - 9y^(2) = 36` |
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