Are the points `(3,4)` and `(2,-6)` on the same or opposite sides of the line `3x-4y=8?`

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

If P is a point (x ,y) on the line y=-3x such that P and the point (3, 4) are on the opposite sides of the line 3x-4y=8, then

For what value (s) of a will the two points (1,a,1) and (-3,0,a) lie on opposite sides of the plane 3x+4y-12z+13=0?

Find the equation of a circle which passes through the points (1,-2) and (4,-3) and whose centre lies on the line 3x+4y=0

Find the range of (alpha,2+alpha) and ((3alpha)/2,a^2) lie on the opposite sides of the line 2x+3y=6.

Find the distance (i) between the points (6,-2) and (-3, 1), (ii) from a point (2, 3) to the line 3x - 4y + 1 = 0, (iii) between the parallel lines 4x + 3y + 1 = 0 and 8x - 6y + 5 = 0.

Find the equation of the circle which passes through the points (1,-2),(4,-3) and whose center lies on the line 3x+4y=7.

Find the distance , (i) Between two points (5,4) and (2,0) (ii) From a point (1,2) to the line 5x+12y-3=0 (iii) Between two parallel lines 3x+4y=12 and 6x+8y+1=0

Find the distance of the point (3,-3) from the line 3x - 4y - 26 = 0

The point (8,-9) with respect to the lines 2x+3y-4=0 and 6x+9y+8=0 lies on the same side of the lines the different sides of the line one of the line none of these