If the point `(2a-3, a^2-1)` is on the same side of the line `x+y-4=0` as that of the origin then

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)) and (x_(2),y_(2)) lie on the same or opposite sides of the line ax+by+c=0, as ax_(1)+by_(1)+c and ax_(2)+by_(2)+c have the same or opposite signs.

The points (1,2) and (3,4) are on the same side of line 2x-3y+5=0

The point (2a-5,a^(2)) lies on the origin side of the line x+y-3=0 if a lies in the interval

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

If the point (1,2) and (34) were to be on the same side of the line 3x-5y+a=0 then

Which one of the points (1, 1), (-1, 2) and (2, 3) lies on the side of the line 4x+3y-5=0 on which the origin lies?

If the points (-2,1),(3,4),( a^(2) ,a) lie on the same side of the straight line 6x-7y-3=0 then "a" can be any number in the interval

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

If the points (4,3) and (cos theta, sin theta) lies same side of the line x+y-1=0 ,then theta lies in which Quadrant?

The sides of a triangle have the combined equation x^(2)-3y^(2)-2xy+8y-4=0. The third side,which is variable,always passes through the point (-5,-1). Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.