For the curve y =` 4x^(3) – 2x^(5)` , find all the points at which the tangent passes through the origin.

Find the point on the curve y = x^(3) – 11x + 5 at which the tangent is y = x – 11.

Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the tangents are parallel to the x-axis.

Find the points on the curve y^(2) - 4xy = x^(2) + 5 for which the tangent is horizontal.

Find the points on the curve y = x 3 at which the slope of the tangent is equal to the y-coordinate of the point.

The point of curve y= 2x^(2) - 6x -4 at which the tangent is parallel to x-axis is

Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.

The slope of the tangent line of a curve is given by 2x^(3)+4x^(2)-3x+2 . Find the equation of the curve if it passes through (0,2).

Find the equation of the normal to the curve x^3+y^3=8x y at the point where it meets the curve y^2=4x other than the origin.