Given `A-=(1,1)` and `A B` is any line through it cutting the x-axis at `Bdot` If `A C` is perpendicular to `A B` and meets the y-axis in `C` , then the equation of the locus of midpoint `P` of `B C` is (a) `x+y=1` (b) `x+y=2` (c) `x+y=2x y` (d) `2x+2y=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

The line (x)/(a)-(y)/(b) =1 cuts the x-axis at P. The equation of the line through P perpendicular to the given line is

Find the equation of the line perpendicular to the line x/a-y/b=1 and passing through a point at which it cuts the x-axis.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

The line 3x+2y=24 meets the y-axis at A and the x-axis at Bdot The perpendicular bisector of A B meets the line through (0,-1) parallel to the x-axis at Cdot If the area of triangle A B C is A , then the value of A/(13) is________

The extremities of latus rectum of a parabola are (1, 1) and (1,-1) . Then the equation of the parabola can be (a) y^2=2x-1 (b) y^2=1-2x (c) y^2=2x-3 (d) y^2=2x-4

If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x-y=0 is theta , then the equation of the line passing through (1, 2) and making an angle theta with the y-axis is (a) x=1 (b) y=2 (c) x+y=3 (d) x-y=3

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0