If \(a, b, c\) are in A.P., then the straight lines \(ax + by + c = 0\) will always pass through ____.
(1, -2)
The line which cuts off equal intercept from the axes and passes through the point \((1, -2)\) is ____.
x + y + 1 = 0
Equations of the lines through the point \((3, 2)\) and making an angle of \(45^\circ\) with the line \(x - 2y = 3\) are ____.
3x - y - 7 = 0, x + 3y - 9 = 0
The points \((3, 4)\) and \((2, -6)\) are situated on the ____ of the line \(3x - 4y - 8 = 0\).
opposite sides
A point moves so that square of its distance from the point \((3, -2)\) is numerically equal to its distance from the line \(5x - 12y = 3\). The equation of its locus is ____.
13(x^2 + y^2) - 83x + 64y + 182 = 0
Locus of the mid-points of the portion of the line \(x \, \sin\theta + y \, \cos\theta = p\) intercepted between the axes is ____.
4x^2 y^2 = p^2 (x^2 + y^2)