Find the equation to the director circle of the hyperbola x2a2−y2b2=1
Director circle is the locus of the point of intersection of the tangents which are right angled.
Let P(h,k) be the point of intersection of two perpendicular tangents.
Equation of pair of tangents is ss1=T2
Comparing this equation with standard pair of line eqution
Since, equation (1) represents two perpendicular line
Coefficient of x2+ coefficient of y2=0