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`

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

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

The lines joining the origin to the points of intersection of the line 3x-2y -1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are

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

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

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

If the lines 2x + 3y + 1 = 0 and 3x - y-4 = 0 lie along two diameters of a circle of circumference 10 pi , then the equation of circle is (i) x^(2) + y^(2) + 2x + 2y + 23 = 0 (ii) x^(2) + y^(2) - 2x - 2y - 23 = 0 (iii) x^(2) + y^(2) - 2 x + 2y - 23 = 0 (iv) x^(2) + y^(2) + 2x - 2y + 23 = 0

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Let P Q R be a right-angled isosceles triangle, right angled at P(2,1)dot If the equation of the line Q R is 2x+y=3 , then the equation representing the pair of lines P Q and P R is (a) 3x^2-3y^2+8x y+20 x+10 y+25=0 (b) 3x^2-3y^2+8x y-20 x-10 y+25=0 (c) 3x^2-3y^2+8x y+10 x+15 y+20=0 (d) 3x^2-3y^2-8x y-15 y-20=0