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  • The equation of the hyperbola whose asymptotes are the straight line <img alt="\mathrm{3 x-4 y+7=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

The equation of the hyperbola whose asymptotes are the straight line \mathrm{3 x-4 y+7=0} and \mathrm{4 x+3 y+1=0} and which passes through origin is 

 

Option: 1

\mathrm{(3 x-4 y+7)(4 x+3 y+1)=0}


Option: 2

\mathrm{12 x^2-7 x y-12 y^2+31 x+17 y=0}


Option: 3

\mathrm{12 x^2-7 x y+2 y^2=0}


Option: 4

none of these 

 


Answers (1)

best_answer

Combined equation of asymptotes is \mathrm{(3 x-4 y+7)(4 x+3 y+1)=0}

\mathrm{\therefore \quad \text { Equation of the hyperbola is }(3 x-4 y+7)(4 x+3 y+1)+K=0}

It passes through origin i.e. (0, 0)     ∴  (7) (1) + K = 0  ∴  K = –7

Hyperbola is \mathrm{(3 x-4 y+7)(4 x+3 y+1)-7=0}

\mathrm{\text { i.e. } 12 x^2-7 x y-12 y^2+31 x+17 y=0}

 

 

Posted by

Ritika Harsh

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