The curve `y=ax^(4)+bx^(2)" with "abgt0`

y= ax + bx^(2)

The curve y=ax^(3)+bx^(2)+cx+5 touches the x -axis at P(-2,0) and cuts the y-axis at the point Q where its gradient is 3. Find the equation of the curve completely.

(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"

Equation of normal to the curve y=ax^(3)+bx^(2)+c , where the curve crosses the Y-axis, is

If the point (1,3) serves as the point of inflection of the curve y=ax^(3)+bx^(2) then the value of 'a' and 'b' are -

If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at (0, 0) but touches x-axis at (1, 0) , then

The curve y=ax^(3)+bx^(2)+cx is inclined at 45^(@) to x-axis at (0,0) but it touches x-axis at (1,0) , then

The curve y=ax^(3)+bx^(2)+cx is inclined at 45^(@) to x-axis at (0,0) but it touches x-axis at (1,0) , then

If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at (0, 0) but touches x-axis at (1, 0) , then