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 line4 x -5 y - K -0 passes through P and Q- for -A- exactly one value of KB- exactly two values of KC- infinitely many values of KD- no value of K

If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
(2005)

Q. 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 \in R),

intersect at the points

P

and

Q

, then the line

4 x + 5 y - K = 0

passes through

P

and

Q

, for :

Q. The system of equations

k x + (k + 1) y + (k - 1) z = 0

(k + 1) x + k y + (k + 2) z = 0

(k - 1) x + (k + 2) y + k z = 0

has a non-trivial solution for

Q. In the xy plane, the segment with end points (3, 8) and (–5, 2) is the diameter of the circle. The point (k, 10) lies on the circle for

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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 :

If the circles $x^{2} + y^{2} + 5 K x + 2 y + K = 0$ and $2 (x^{2} + y^{2}) + 2 K x + 3 y - 1 = 0, (K \in R),$ intersect at the points $P$ and $Q$ , then the line $4 x + 5 y - K = 0$ passes through $P$ and $Q$ , for :