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If hyperbola \mathrm{x^2-y^2=a^2}  and \mathrm{x y=c^2}  are of same size, then 

 

Option: 1

\mathrm{c^2=2 a^2}


Option: 2

\mathrm{c=2 a}


Option: 3

\mathrm{2 c^2=a^2}


Option: 4

none of these

 


Answers (1)

best_answer

Distance between their vertices will remain same (length of transverse axis) 2a is distance between vertices is 1st  hyperbola (c, c) and (–c, –c) are vertices of 2nd .

\mathrm{2 a=\sqrt{(c+c)^2+(c+c)^2} \Rightarrow 2 a=2 \sqrt{2} c \Rightarrow a^2=2 c^2}

 

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