The locus of the point of intersection of perpendicular tangents to the ellipse is called

Step-by-step solution

The equation of a pair of tangents from ( , ) to the ellipse x² a² + y² b² =1 is ( x² a² + y² b² -1 ) ( ² a² + ² b² -1 )= ( x a² + y b² -1 )² ( SS ₁= T ² ) The tangents are perpendicular, if the coefficient of x²+ the coefficient of y²=0 . array r 1 a² ( ² a² + ² b² -1 )- ² a⁴ + 1 b² ( ² a² + ² b² -1 ) - ² b⁴ =0 array gathered ² a² b² - 1 a² + ² a² b² - 1 b² =0 ²+ ²=a² b² ( 1 a² + 1 b² ) =a² b² ( a²+b² a² b² ) =a²+b² gathered Hence, the locus of ( , ) is the circle x²+y²=a²+b² This circle is called the director cir