If the eccentricity of the hyperbola x2-a2-y2-b2-1 is 5-4 and 2 x-3 y-6-0 is focal chord of the hyperbola- then the length of transverse axis is

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Standard XII

Mathematics

Four Common Forms of Parabola Equation

If the eccent...

Question

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

12/5

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24/5

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6/5

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5/24

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Solution

The correct option is B
24/5

Focus(ae,0) lies on the line 2x +3y -6 = 0 therefore ae = 3 $\Rightarrow$ 2a = $\frac{12}{5}$

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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 ____________

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 ___ .

Q. If the eccentricity of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\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 ____

Q. If the eccentricity of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 is d \frac{5}{4} and 2 x + 3 y - 6 = 0

is the focal chord of the hyperbola, then the length of transverse axis is equal to

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If the eccentricity of the hyperbola x2a2−y2b2=1 is 54 and 2x + 3y – 6 = 0 is focal chord of the hyperbola, then the length of transverse axis is

The correct option is B 24/5 Focus(ae,0) lies on the line 2x +3y -6 = 0 therefore ae = 3 ⇒ 2a = 125

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

The correct option is B
24/5

Focus(ae,0) lies on the line 2x +3y -6 = 0 therefore ae = 3 $\Rightarrow$ 2a = $\frac{12}{5}$