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A hyperbola passes through the points $(3,2)$ and $(-17,12)$ and has its centre at origin and transverse axis is along $x$-axis. The length of its transverse axis is
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$2$
Let the equation of hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
But it passes through $(3,2) \Rightarrow \frac{9}{a^2}-\frac{4}{b^2}=1$ ....(i)
Also its passes through $(-17,12)$
$\Rightarrow \quad \frac{(-17)^2}{a^2}-\frac{(12)^2}{b^2}=1$ ....(ii)
Solving these, we get $a=1$ and $b=\sqrt{2}$
Hence length of transverse axis $=2 a=2$.
But it passes through $(3,2) \Rightarrow \frac{9}{a^2}-\frac{4}{b^2}=1$ ....(i)
Also its passes through $(-17,12)$
$\Rightarrow \quad \frac{(-17)^2}{a^2}-\frac{(12)^2}{b^2}=1$ ....(ii)
Solving these, we get $a=1$ and $b=\sqrt{2}$
Hence length of transverse axis $=2 a=2$.
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