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

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 equation of the bisectors of the angles between the lines joining the origin to the point of intersection of the straight line x-y=2 with the curve 5x^2+11 x y+8y^2+8x-4y+12=0

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) .

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

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

The area of the triangle formed by joining the origin to the points of intersection of the line sqrt5x+2y=3sqrt5 and circle x^2+y^2=10 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 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

The points of intersection of the line 4x-3y-10=0 and the circle x^2+y^2-2x+4y-20=0 are ________ and ________