Question

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

• A. $9x-3y+2=0$
• B. $2x-y+1=0$
• C. $x-2y+8=0$
• D. $x-y+2=0$

Answer 1

The correct option is D $x-y+2=0$

Any tangent to $y^2=8x\text{is}y=mx+\frac{2}{m}$
This intersects $xy=-1$ where $-\frac{1}{x}=mx+\frac{2}{m}$
$\Rightarrow m^2{x}^{2}2+2x+m=0$
For tangency, $D=4-4m^3=0\Rightarrow m=1$
$\Rightarrow$ Tangent is x - y + 2 = 0