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

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 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

A family of chords of the parabola y^2=4ax is drawn so that their projections on a straight line inclined equally to both the axes are all of a constant length c, prove that the locus of their middle points is the curve (y^2-4ax)(y+2a)^2+2a^2c^2=0 .

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

ABC 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 ABC is (a)(x-1)^(2)+y^(2)=4(b)x+y=3( c) 2x-y=0 (d) none of these

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

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 y=x+2 .

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

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