If the circles x 2 + y 2 + 5 K x + 2 y + K = 0 and 2 x 2 + y 2 + 2 K x + 3 y - 1 = 0 , K ∈ R , intersect at the points P and Q, then the line 4 x + 5 y - K = 0 , passes through P and Q , for:

Step-by-step solution

S 1 = x 2 + y 2 + 5 K x + 2 y + K = 0 S 2 = x 2 + y 2 + K x + y 2 + 1 2 = 0 ∴     Equation of common chord is S 1 - S 2 = 0 ⇒     4 K x + 3 2 y + K - 1 2 = 0           . . . . 1 Give equation of common chord is 4 x - 5 y - K = 0         . . . . 2 ∵   1   &   2 are identical ∴       4 K 4 = 3 2 - 5 = K - 1 2 - K Clearly, no value of K satisfy simultaneously.