At a point `(x_1,y_1)` on the curve `x^3+y^3=3axy`, show that the tangent is `(x_1^2-ay_1)x+(y_1^2-ax_1)y=ax_1y_1`.

At the point (x_(1),y_(1)) on the curve x^(3)+y^(3)=3axy show that the tangent is (x_(1)^(2)-ay_(1))x+(y_(1)^(2)-ax_(1))y=ax_(1)y_(1)

The angle which the tangent at (2,1) to the curve x^3+y^3=9 with the x-axis is

The points on the curve 2a^2y=-x^3-3ax^2 at which the tangent is perpendicular to y-axis is

If the tangent at (x_(0),y_(0)) to the curve x^(3)+y^(3)=a^(3) meet the curve again at (x_(1)y_(1)) prove that (x_(1))/(x_(0))+(y_(1))/(y_(0))=-1

If at any point (x_1, y_1) on the curve y=f(x) the lengths of the subtangent and subnormal are equal, then the length of the tangent drawn to that curve at that point is

Show that the tangent at P(x_(1),y_(1)) on the curve sqrt(x)+sqrt(y)=sqrt(a) " is " x""x_(1)^((-1)/2)+yy_(1)^((-1)/2)=a^(1/2)

The point on the curve y=x^3+x-2 , the tangent at which is parallel to the line y=4x-1 is