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`

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

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) =

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 point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

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 point(s) of intersection of the line 2x + 3y = 18 and the circle x^2 + y^2 = 25

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)

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

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x+2y+z=10 at

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