A pair of perpendicular straight lines is drawn through the origin forming with the line `2x+3y=6` an isosceles triangle right-angled at the origin. The equation to the line pair is
(a) `5x^2-24 x y-5y^2=0`
(b)`5x^2-26 x y-5y^2=0`
(c)`5x^2+24 x y-5y^2=0`
(d)`5x^2+26 x y-5y^2=0`

Find the equation of a line passing through origin and parallel to the line 3x-5y+2=0 .

The equation of the line joining the origin to the point of intersection of the lines 2x^2+xy-y^2+5x-y+2=0 is

Equation of a straight line passing through the origin and making with x-axis an angle twice the size of the angle made by the line y=0. 2 x with the x-axis, is : (a) y=0. 4x (b) y=(5/(12))x (c) 6y-5x=0 (d) None of these

The equation of the circle passing through the point of intersection of the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is (a) 5x^2+5y^2+18 x+6y-5=0 (b) 5x^2+5y^2+9x+8y-15=0 (c) 5x^2+5y^2+4x+9y-5=0 (c) 5x^2+5y^2-4x-2y-18=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+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

Find the equation of a straight line through the point of intersection of the lines 4x-3y=0\ a n d\ 2x-5y+3=0 and parallel to 4x+5y+6=0.

Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0 . Distance between the orthocenter and the circumcenter of triangle ABC is

Find the equation of the common chord of the following pair of circles x^2+y^2-4x-4y+3=0 x^2+y^2-5x-6y+4=0

Find the equation of the line through the point of intersection of, the lines x-3y + 1 = 0 and 2x + 5y-9-0 and whose distance from the origin is sqrt5

Find the equation of the line through the point of intersection of, the lines x-3y + 1 = 0 and 2x + 5y-9-0 and whose distance from the origin is sqrt5