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 `2x y=c^2` (b) `x y+c^2=0` `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=2 (c) x+y=2 (d) none of these

Let AB be a line segment of length 4 with A on the line y = 2x and B on the line y = x . The locus of the middle point of the line segment is

Let AB be a line segment of length 4 with A on the line y = 2x and B on the line y = x . The locus of the middle point of the line segment is

Let AB be a line segment of length 4 with A on the line y = 2x and B on the line y = x . The locus of the middle point of the line segment is

The area of the smaller portion of the circle x^2+y^2=4 cut off the line x+y=2 is

A line moves in such a way that the sum of the intercepts made by it on the axes is always c. The locus of the mid- point of its intercept between the axes is (A) x+y =2c (B) x+y=c (C) 2(x+y)=c (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

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

Find the coordinates of the middle point of the chord which the circle x^2 +y^2 + 4x-2y-3=0 cuts off on the line x-y+2=0

A B C is a variable triangle such that A is (1, 2), and Ba n dC on the line y=x+lambda(lambda is a variable). Then the locus of the orthocentre of "triangle"A B C is x+y=0 (b) x-y=0 x^2+y^2=4 (d) x+y=3