Is the point `(2,-7)` lies on origin side of the line `2x+y+2 = 0` ?

The equation of the line joining the point {3, 5) to the point of intersection of the lines 4x + y - 1 = 0 and 7x - 3y - 35 = 0 is equidistant from the points (0,0) and (8,34) .

The point (1,2) lies inside the circle x^(2) + y^(2) - 2x + 6y + 1 = 0 .

The point A(2,7) lies on the perpendicular bisector of the line segment joining the points P(6,5) and Q(0,-4).

Equations of the lines through the point (3, 2) and making an angle of 45° with the line x-2y + 3=0 are ….... .

The distance of the point of intersection of the lines 2 x- 3y + 5 = 0 and 3x + 4y =0 from the line 5x-2y =0 is

Find the equations of the lines through the point of intersection of the lines x - y + 1 = 0 and 2x - 3y + 5 =0 and whose distance from the point (3,2) is (7)/(5) .

Find the equation of the circle which passes through the point (2,-2), and (3,4) and whose centre lies on the line x+y=2 .

The three sides of a triangle are given by (x^2 - y^2)(2x+3y-6) = 0 . If the points (-2,a) lies inside and (b,1) lies outside the triangle, then

Prove that 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 are at right angles.

Find equation of the circle passes through points (2,3) and (4,5) whose centre lies on the line y - 4x + 3 = 0.