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 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)+4xy-1=0(b)x^(2)+5y^(2)+4xy+1=0(b)x^(2)+5y^(2)+4xy+1=0(c)x^(2)+5y^(2)+4xy-1=0(d)4x^(2)+5y^(2)+4xy+1=0

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Q. the equation of image of the pair of lines y=|2x-1| in y-axis is (A) 4x^2-y^2-4x+1=0 (B) 4x^2-y^2+4x+1=0 (C) 4x^2+y^2+4x+1=0 (D) 4x^2+y^2-4x+1=0

From the points (3,4), chords are drawn to the circle x^(2)+y^(2)-4x=0 .The locus of the midpoints of the chords is (a) x^(2)+y^(2)-5x-4y+6=0(b)x^(2)+y^(2)+5x-4y+6=0(c)x^(2)+y^(2)-5x+4y+6=0(d)x^(2)+y^(2)-5x-4y-6=0

The equation of the circle having the intercept on the line y+2x=0 by the circle x^2 + y^2 + 4x + 6y = 0 as a diameter is : (A) 5x^2 + 5y^2 - 8x + 16y =0 (B) 5x^2 + 5y^2 + 8x - 16y =0 (C) 5x^2 + 5y^2 - 8x - 16y =0 (D) 5x^2 + 5y^2 + 8x+- 16y =0

Find the point of intersection of the lines 2x-3y+8=0 and 4x+5y=6

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Image of the locus of R in the line y = - x is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

The equation of the line through the intersection of the lines 2x-3y=0 and 4x-5y=2 and