The equation of rectangular hyperbola $x y = c^{2}$ is drawn by rotating $x^{2} - y^{2} = 35$ and its asymptote is the coordinate axis, then value of $c$ is

\pm \frac{35}{2}

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\pm \sqrt{\frac{35}{2}}

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\pm \sqrt{35}

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\pm \frac{\sqrt{35}}{2}

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Solution

The correct option is B $\pm \sqrt{\frac{35}{2}}$
The equation of rectangular hyperbola $x y = c^{2}$ is drawn by rotating $x^{2} - y^{2} = a^{2}$ , then $c^{2} = \frac{a^{2}}{2}$
$c^{2} = \frac{35}{2} \Rightarrow c = \pm \sqrt{\frac{35}{2}}$
Hence, the correct answer is option (a).

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Similar questions

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Which of the following statements are correct?

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2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
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The equation of rectangular hyperbola xy=c2 is drawn by rotating x2−y2=35 and its asymptote is the coordinate axis, then value of c is

The correct option is B ±√352The equation of rectangular hyperbola xy=c2 is drawn by rotating x2−y2=a2, then c2=a22 c2=352⇒c=±√352 Hence, the correct answer is option (a).

The equation of rectangular hyperbola $x y = c^{2}$ is drawn by rotating $x^{2} - y^{2} = 35$ and its asymptote is the coordinate axis, then value of $c$ is

The correct option is B $\pm \sqrt{\frac{35}{2}}$
The equation of rectangular hyperbola $x y = c^{2}$ is drawn by rotating $x^{2} - y^{2} = a^{2}$ , then $c^{2} = \frac{a^{2}}{2}$
$c^{2} = \frac{35}{2} \Rightarrow c = \pm \sqrt{\frac{35}{2}}$
Hence, the correct answer is option (a).