If the lines joining the origin and the point of intersection of curves `a x^2+2h x y+b y^2+2gx+0` and `a_1x^2+2h_1x y+b_1y^2+2g_1x=0` are mutually perpendicular, then prove that `g(a_1+b_1)=g_1(a+b)dot`

The pair of lines joining the origin to the points of intersection of the curves ax^2+2hxy+by^2+2gx=0 and a'x^2+2h'xy+b'y^2+2g'x=0 will be at right angles to one another , if

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 of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

The product of the perpendiculars from origin to the pair of lines a x^2+2h x y+b y^2 + 2gx + 2fy + c =0 is

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)

If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find the value of adot

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2