The equation of the common tangent drawn to the curves y^2=8 x and x y=-1 is

Step-by-step solution

Let P (t, -1 t ) be a point on x y=-1 Equation of tangent of P aligned & = 1 2 [x ( -1 t )+x y ]=-1-x+t^2 y=-2 t & y= x t^2 + 2 t aligned This is also at tangent of y^2=8 x aligned & i.e. c= a m & 2 t = 2 1 t^2 & t^3=1 & t=1 aligned Hence, the equation of common tangent aligned & y= x 1 + 2 1 & y=x+2 aligned