A point P moves such that the chord of contact of P with respect to the circle x 2 + y 2 = 4 passes through the point 1 , 1 . The coordinates of P when it is nearest to the origin are

Step-by-step solution

Let, the point P be a , b then Equation of the chord of contact is x a + y b = 4 Since, it passes through 1 , 1 so, a + b = 4 ⇒ x + y = 4 is the locus of the point P . Hence, the nearest point on x + y = 4 is 2 , 2 .