If ` a > 0 and b^2 - 4ac = 0`, then the graph of ` y = a x^2 + bx + c` touches x-axis and lies above x-axis.

If a>0 and b^(2)-4ac<0, then the graph of y=ax^(2)+bx+c

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If the graph of y=ax^(2)+bx+c lies completely above the x-axis, then

If the graph of y=ax^(2)+bx+c lies completely above the x-axis, then

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

The value of k if x^2+y^2+4x-6y-k=0 to touch y-axis is

Let f(x)=ax^(2)+bx + c , where a in R^(+) and b^(2)-4ac lt 0 . Area bounded by y = f(x) , x-axis and the lines x = 0, x = 1, is equal to :