Locus of the mid-points of the chords of contact of x 2 + y 2 = 2 from the points on the line 3 x + 4 y = 10 is a circle with centre C . If O be the origin, then 2 O C is equal to

Step-by-step solution

Equation of the chord with mid point h , k is h x + k y = h 2 + k 2 … . i Equation of the chord with mid point ( x 1 , y 1 ) is x x 1 + y y 1 = 2 … … i i On comparing ( i )   &   ( ii ) , we get x 1 = 2 h h 2 + k 2 and y 1 = 2 k h 2 + k 2 x 1 , y 1 lies on 3 x + 4 y = 10 ⇒ 6 h + 8 k = 10 h 2 + k 2 ∴ locus of h , k is x 2 + y 2 - 3 5 x - 4 5 y = 0 Which is a circle with centre C = 3 10 , 4 10 ∴ O C = 1 2