Find the co-ordinates of that point on the curve `x^(3)+y^(3)= a^(3)` at which the tangent drawn is parallel to X-axis.

Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(2) = 1 at which the tangent drawn is parallel to Y-axis.

Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(2) = 1 at which the tangent drawn is parallel to Y-axis.

Find the co-ordinates of that point on the curve y^(2)=x^(2)(1-x) at which the tangent drawn is perpendicular to X-axis.

Find the co-ordinates of that point on the curve y^(2)=x^(2)(1-x) at which the tangent drawn is perpendicular to X-axis.

Using Lagrange's Mean Value theorem , find the co-ordinates of a point on the curve y = x^(3) at which the tangent drawn is parallel to the chord joining the points (1,1) and (3,27).

Using Lagrange's Mean Value theorem , find the co-ordinates of a point on the curve y = x^(2) at which the tangent drawn is parallel to the line joining the points (1,1) and (3,9).

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 x^(2) + y^(2) - 2x - 3 = 0 at which the tangents are parallel to X-axis.

A point on the curve y= x^(3)-3x + 5 at which the tangent line is parallel to y= -2x is