The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4 x-5 y=20 to the circle x²+y²=9 is

Step-by-step solution

Any point P on line 4 x-5 y=20 can be considered as ( , 4 -20 5 ) . Equation of chord of contact A B to the circle x²+y²=9 drawn from point P ( , 4 -20 5 ) is x. + y. ( 4 -20 5 )=9...(i) Also the equation of chord A B whose mid point is (h, k) is h x+k y=h²+k²....(ii) Equations (i) and (ii) represent the same line, h = k 4 -20 5 = h²+k² 9 5 k =4 h -20 h and 9 h= (h²+k² ) = 20 h 4 h-5 k and = 9 h h²+k² 20 h 4 h-5 k = 9 h h²+k² 20 (h²+k² )=9(4 h-5 k) Locus of (h, k) is 20 (x²+y² )-36 x+45 y=0