Equation of tangent to parabola $y^2=8x$ which is also tangent to $xy=-1$ is
Step-by-Step Solution
Key Concept: Tangent to $y^2=8x$: $y=mx+2/m$; also tangent to $xy=-1$ (rectangular hyperbola)
$y=mx+2/m$ tangent to $xy=-1$: sub $y=mx+2/m$ into $xy=-1$: $x(mx+2/m)=-1\Rightarrow mx^2+2x/m+1=0$. Discriminant$=0$: $4/m^2-4m=0\Rightarrow 1/m^2=m\Rightarrow m^3=1\Rightarrow m=1$. $y=x+2$. Also $m=-1$: $y=-x-2$ (check).
Correct Answer: 3