A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area `c^2dot` Then the locus of the middle point of the line is (a)`2x y=c^2` (b) `x y+c^2=0` (c)`4x^2y^2=c` (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

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

Show that the straight line x^2-4xy+y^2=0 and x + y = 3 form an equilateral triangle.

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

A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation. a. x^2+5y^2+4x y-1=0 b. x^2+5y^2+4x y+1=0 c. x^2+5y^2-4x y-1=0 d. 4x^2+5y^2+4x y+1=0

Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x^2-9y^2 +30 = 0 (b) 4x^2-9y^2-30 = 0 (c) 9x^2-4y^2-30=0 (d) none of these

The center of a rectangular hyperbola lies on the line y=2xdot If one of the asymptotes is x+y+c=0 , then the other asymptote is (a) 6x+3y-4c=0 (b) 3x+6y-5c=0 (c) 3x-3y-c=0 (d) none of these

Find the equation of straight line joining the points of intersection of the lines 3x+2y+1=0 and x+y=3 to the intersection of the lines y-x=1 and 2x+y+2=0

A ray of light travels along a line y=4 and strikes the surface of curves y^2=4(x+y)dot Then the equations of the line along which of reflected ray travels is x=0 (b) x=2 (c) x+y (d) 2x+y=4