Question

If the circles x² + y² + 5Kx + 2y + K = 0 and 2(x² + y²) + 2Kx + 3y – 1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q for:
(A) exactly one value of K (B) not value of K
(C) infinitely many values of K (D) exactly two values of K

Answer 1

Step-by-step explanation:

equation of common chord 4 kx + 1/2 y + k + 1/2 = 0 ..(i) and given line 4x + 5y - k = ...(ii) on comparing (i) & (ii) we get k = 1/10 = k + 1/2/-k No. real value of k exist Read more on Sarthaks.com - https://www.sarthaks.com/367148/if-the-circles-2-y-2-5kx-2y-k-0-and-2-x-2-y-2kx-3y-1-0-kr-intersect-at-the-points-p-and-q-then-the-line