If the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is $\frac{5}{4}$ and $2 x + 3 y - 6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to ____________

$\frac{12}{5}$

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$\frac{24}{5}$

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$\frac{6}{5}$

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$\frac{5}{24}$

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Solution

The correct option is B
$\frac{24}{5}$

$e = \frac{5}{4}, 2 a e = 6 \Rightarrow a = \frac{12}{5}$

So, length of the transverse axis = $\frac{24}{5}$

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If the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is 5/4 and 2x+3y-6 = 0 is a focal chord of the hyperbola, then the length of the transverse axis is equal to ___ .

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If the eccentricity of the hyperbolax2a2−y2b2=1 is54 and 2x+3y–6=0 is a focal chord of the hyperbola, then the length of transverse axis is equal to ____________

The correct option is B 245 e=54,2ae=6⇒a=125 So, length of the transverse axis = 245

If the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is $\frac{5}{4}$ and $2 x + 3 y - 6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to ____________

The correct option is B
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So, length of the transverse axis = $\frac{24}{5}$