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  • The equations of the transverse and conjugate axes of a hyperbola are respectively x + 2y − 3 = 0, 2x − y + 4 = 0, and their respective lengths are <img alt="

The equations of the transverse and conjugate axes of a hyperbola are respectively x + 2y − 3 = 0, 2x − y + 4 = 0, and their respective lengths are \mathrm{\sqrt{2} \text { and } 2 / \sqrt{3} \text {. }} The equation of the hyperbola is

 

Option: 1

\mathrm{\frac{2}{5}(x+2 y-3)^2-\frac{3}{5}(2 x-y+4)^2=1}


Option: 2

\mathrm{\frac{2}{5}(2 x-y+4)^2-\frac{3}{5}(x+y-3)^2=1}


Option: 3

\mathrm{2(2 x-y+4)^2-3(x+2 y-3)^2=1}


Option: 4

\mathrm{2(x+2 y-3)^2-3(2 x-y+4)^2=1}


Answers (1)

best_answer

The equation of the hyperbola is 

\mathrm{\begin{aligned} &\frac{\left(\frac{2 x-y+4}{\sqrt{5}}\right)^2}{1 / 2}-\frac{\left(\frac{x+2 y-3}{\sqrt{5}}\right)^2}{1 / 3}=1\\ &\frac{2}{5}(2 x-y+4)^2-\frac{3}{5}(x+2 y-3)^2=1 \end{aligned}}

 

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seema garhwal

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