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`

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a x^2-2h x y-b y^2=0 b x^2-2h x y+a y^2=0 b x^2+2h x y+a y^2=0 a x^2-2h x y+b y^2=0

Find the equation of the pair of straight lines passing through the point (1,3) and perpendicular to the lines 2x-3y+1=0 and 5x+y-3=0.

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=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

Show that straight lines joining the origin to the points of intersection of 3x-2y+2=0 and 3x^2+5x-2y^2+4x+5y=0 are at right angles .

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0