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  • The equation of the common tangent to the curves <img alt="y^2=8 x \text { and } x y=-1" src="https://entrancecorner.oncodecogs.com/gif.latex?y%5E2%3D8%20x%20%5Ctext%20%7B%20and%20%7D%20x

The equation of the common tangent to the curves y^2=8 x \text { and } x y=-1  is 

Option: 1

\begin{aligned} & 3 y=9 x+2 \\ \end{aligned}


Option: 2

y=2 x+1 \\


Option: 3

2 y=x+8 \\


Option: 4

y=x+2


Answers (1)

best_answer

Tangent to the curve  y^2=8 x \text { is } y=m x+\frac{2}{m}   So, it must satisfy xy=-1

Since, it has equal roots.

\begin{aligned} & \therefore \mathrm{D}=0 \\ & \Rightarrow \frac{4}{m^2}-4 m=0 \\ & \Rightarrow m^3=1 \\ & \Rightarrow m=1 \end{aligned}

Hence, equation of common tangent is y=x+2

Posted by

Divya Prakash Singh

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