If the circle x2 - y2 - 52Kx - 2y - K - 0 and 2x2 - 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 $x^{2} + y^{2} + 2 a x + c y + a = 0 a n d x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P andn Q then the line 5x + by - a = 0 passes through P and Q for
(2005)

Q. The value of

k

so that

x^{2} + y^{2} + k x + 4 y + 2 = 0

and

2 (x^{2} + y^{2}) - 4 x - 3 y + k = 0

cut orthogonally is:

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If the circle x2+y2+52Kx+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:

The correct option is B no value of KEquation of common chord4kx+12y+k+12=0 ...(1)and given line is 4x+5y−k=0 ...(2)On comparing (1) & (2), we getk=110=k+12−k

If the circle $x^{2} + y^{2} + 52 K x + 2 y + K = 0$ 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:

The correct option is B no value of $K$
Equation of common chord
$4 k x + \frac{1}{2} y + k + \frac{1}{2} = 0$ ...(1)
and given line is $4 x + 5 y - k = 0$ ...(2)
On comparing (1) & (2), we get
$k = \frac{1}{10} = \frac{k + \frac{1}{2}}{- k}$