The normal at any point `P(x_1,y_1)` of curve is a line perpendicular to tangent at the point `P(x_1,y_1)`. In case of rectangular hyperbola `xy=c^2`, the equation of normal at `(ct,(c )/(t))` is `xt^3-yt-ct^4+c=0`. The shortest distance between any two curves always along the common normal.
If normal at (5, 3) of rectangular hyperbola `xy-y-2x-2=0` intersect it again at a point:

Options

A. `(-1,0)`
B. `(-1,1)`
C. `(0,-2)`
D. `((3)/(4),-14)`

Answer

D