A chord PQ of an ellipse subtends a right angle at the centre of the ellipse .Show that the point of intersection of tangents at P and Q lies on the ellipse
Let the tangents at P and Q intersects at ,then PQ is the chord of tangents drawn from
The equation of the pair of lines CP and CQ is obtained by homogenising the equation of S=0 with PQ.
The combined equation is
But angle PCQ is 90.
Therefore,the coefficients of square of x and square of y is equal to zero.
Hence the point of intersection of tangents at P and Q lies on the ellipse