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  • The equation ef the coenmine tangent to the curves <img alt="\mathrm{y^2-3 x\: and \: x y=-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%5E2-3%20x%5C%3A%20and%20%5C%3A%20x%

The equation ef the coenmine tangent to the curves \mathrm{y^2-3 x\: and \: x y=-1} is
 

Option: 1

\mathrm{3 y=7 x+7}
 


Option: 2

\mathrm{y=2 x+1}
 


Option: 3

\mathrm{2 y=x+a}
 


Option: 4

\mathrm{y=x+2}


Answers (1)

best_answer

Tangent to the curve \mathrm{y^2=8 x\: is \: y=m x+\frac{2}{m}}, where \mathrm{' m '} is slope of tangent, this tangent also touches \mathrm{x y=-1}at one point.

\mathrm{ \Rightarrow x\left(m x+\frac{2}{m}\right)=-1 \Rightarrow m x^2+\frac{2}{m} x+1=0 }

\mathrm{ \Rightarrow\left(\frac{2}{m}\right)^2-4 \cdot m \cdot 1=0 \text { (since, it has equal roots)} }

\mathrm{ \Rightarrow\left(\frac{2}{m}\right)^2-4 m=0 \Rightarrow 4-4 m^3=0 }

\mathrm{ \therefore m=1 }

\mathrm{ \Rightarrow \text { Equation of tangent is } y=x+2 . }






 

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