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 `3x^2+8x y-3y^2=0` `3x^2+10 x y+3y^2=0` `y^2+2x y-3x^2=0` `x^2+2x y-3y^2=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 (1) 3x^2+8x y-3y^2=0 (2) 3x^2+10 x y+3y^2=0 (3) y^2+2x y-3x^2=0 (4) x^2+2x y-3y^2=0

The point of intersection of the two lines given by 2x^2-5xy +2y^2-3x+3y+1=0 is

Find the equation of the common chord of the following pair of circles x^2+y^2+2x+3y+1=0 x^2+y^2+4x+3y+2=0

The lines 2x + y -1=0 , ax+ 3y-3=0 and 3x + 2y -2=0 are concurrent for -

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 5x^2-24 x y-5y^2=0 5x^2-26 x y-5y^2=0 5x^2+24 x y-5y^2=0 5x^2+26 x y-5y^2=0

The equation of the medians of a triangle formed by the lines x+y-6=0, x-3y-2=0 and 5x-3y+2=0 is

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

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

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , then find the equation of the circle on A B as diameter.

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is