The curve `y=a x^3+b x^2+c x+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.

The curve ay^2=x^2(3a-x) cuts the y - axis at .........

Find the asymptotes of the curve x y-3y-2x=0 .

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 circle x^2 + y^2 - 3x - 4y + 2 = 0 cuts the x axis at the points

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

A circle touches the y axis at (0,2) and its x intercept equal to 3 units, then the equation of the circle is

A curve C passes through (2,0) and the slope at (x , y) as ((x+1)^2+(y-3))/(x+1)dot Find the equation of the curve.

A curve with equation of the form y=a x^4+b x^3+c x+d has zero gradient at the point (0,1) and also touches the x- axis at the point (-1,0) then the value of x for which the curve has a negative gradient are:

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

Find the equations of tangent and normal to the curve y^(2)-4x-2y+5=0 at the point where it cuts the x-axis.