The image of `P(a ,b)` on the line `y=-x` is `Q` and the image of `Q` on the line `y=x` is `R` . Then the midpoint of `P R` is (a) `(a+b ,b+a)` (b) `((a+b)/2,(b+2)/2)` (c) `(a-b ,b-a)` (d) `(0,0)`

Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary point P on the line x+y=25 . The locus of the midpoint of chord A B is

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

If (x, y) is any point on the line joining the points A(a, 0) and B (0, b), then show that (x)/(a)+(y)/(b) = 1

The equation of the line AB is y = x . If A and B lie on the same side of the line mirror 2x-y = 1 , then the equation of the image of AB is (a) x+y-2=0 (b) 8x+y-9=0 (c) 7x-y-6=0 (d) None of these

P and Q are points on the line joining A(-2,5) and B(3,1) such that A P=P Q=Q B . Then, the distance of the midpoint of P Q from the origin is (a) 3 (b) (sqrt(37))/2 (c) 4 (d) 3.5

Show that the reflection of the line a x+b y+c=0 on the line x+y+1=0 is the line b+a y+(a+b-c)=0 where a!=bdot

The condition on a and b , such that the portion of the line a x+b y-1=0 intercepted between the lines a x+y=0 and x+b y=0 subtends a right angle at the origin, is (a) a=b (b) a+b=0 (c) a=2b (d) 2a=b

In a three-dimensional coordinate system, P ,Q , and R are images of a point A(a ,b ,c) in the x-y ,y-z and z-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle AOG is ( O is the origin) (A) 0 (B) a^2+b^2+c^2 (C) 2/3(a^2+b^2+c^2) (D) none of these

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The area of a parallelogram formed by the lines a x+-b x+-c=0 is (a) (c^2)/((a b)) (b) (s c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these