The Line P = x  become Tangent To  if  

The point of intersection of two perpendicular tangents to  lies on the circle

The curve for which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is

The curve for which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is

The product of perpendicular drawn from any point on the hyperbola to its asymptotes is

The locus of the point of intersection of the lines 

, where m is a parameter, is always

The condition that the straight line lx + my = n may be a normal to the hyperbola b²x² – a²y² = a²b² is

If the eccentricities of the hyperbolas  and  be eand e₁, then