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

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 angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

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

Prove that the pair of straight lines joining the origin to the points of intersection of the circles x^2+y^2=a and x^2+y^2+2(gx+fy)=0 is a^(prime)(x^2+y^2)-4(gx+fy)^2=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

Find the condition for which the lines joining the origin to the points of intersection of the line y= mx+c and the circle x^2+y^2=a^2 will be mutually bot

The pair of straight lines joining the origin to the points of intersection of X^2+Y^2=4 and y=3X +c are perpendicular, if frac(c^2)(4) =

Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

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