" For what value of a the curve "y=x^(2)+ax+25" touches the "x" -axis: "

The tangent to the curve 2a^(2)y=x^(3)-3ax^(2) is parallel to the x -axis at the points

(i) If the tangent to the curve xy+ax+by=0 at (1,1) is inclined at an angle tan^(-1) 2 with positive x-axis in anticlockwise then find a and b? (ii) The curve y=ax^(3) +bx^(2)+3x+5" touches "y=(x+2)^(2) " at "(-2,0) " then "|(a)/(2)+b|" is"

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 equation of tangent to the curve y=x+(4)/(x^2) , that is parallel to the x-axis is y = k. Then the value of k 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

If the curves y=ax^(3)-3ax+4a and y=12x+4a touches at x=0 then a =