For what value of a, the curve `y=x^2+ax+25` touches the x-axis

For what value of 'a' is the area bounded by the curve y=a^(2)x^(2)+ax+1 and the straight line y=0.x=0 and x=1 the least?

The number of values of c such that the line y=4 x+c touches the curve (x^(2))/(4)+y^(2)=1 is

Select the correct option from the given alternatives. If the circle x^2+y^2-6x-8y+(25-k^2)=0 touches the Y-axis then the value of k is

Find the value of a,b,c such that curves y=x^(2)+ax+bandy=cx-x^(2) will touch each other at the point (1,0)

Find the area bounded by the curve y = x^(2) - 2x + 5 , the tangent to it at the point (2,5) and the axes of the coordinates.

The curve y = ax ^(3) + bx ^(2) + cx + 5 touches the x-axis at P (-2, 0) and cuts the y-axis at a point Q where its gradient is 3, then 2a + 4b is equal to :