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. The two circles

x^{2} + y^{2} + 2 a x - c^{2} = 0

and

x^{2} + y^{2} + 2 a b x - c^{2} = 0

meet in points P and Q. Parallel lines are drawn through P and Q meet the circles in point R and S. Prove that the locus of mid-point of RS is the circle.

x^{2} + y^{2} + (a + b) x = 0

Q. 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:

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If the circles x2+y2+2ax+cy+a=0 and x2+y2−3ax+dy−1=0 interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for (2005)

The correct option is B no value of a S1=x2+y2+2ax+cy+a=0 S2=x2+y2−3ax+dy−1=0 Equation of radical axis of S1 and S2 S1−S2=0⇒5ax+(c−d)y+a+1=0 Given that 5x+by−a=0 passes through P and Q ⇒a1=c−db=a+1−a⇒a+1=−a2 ⇒a2+a+1=0 ⇒a∉R. Not real value of a.

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)