If the tangent at `(x_1,y_1)` to the curve `x^3+y^3=a^3` meets the curve again in `(x_2,y_2),` then prove that `(x_2)/(x_1)+(y_2)/(y_1)=-1`

If the tangent at (x_(0),y_(0)) to the curve x^(3)+y^(3)=a^(3) meets the curve again at (x_(1),y_(1)) , then (x_(1))/(x_(0))+(y_(1))/(y_(0)) is equal to

If the tangent at P(1,1) on the curve y^(2)=x(2-x)^(2) meets the curve again at A , then the points A is of the form ((3a)/(b),(a)/(2b)) , where a^(2)+b^(2) is

The tangents from (2,0) to the curve y=x^(2)+3 meet the curve at (x_(1),y_(1)) and (x_(2),y_(2)) then x_(1)+x_(2) equals

If the tangent at (1,1) on y^(2)=x(2-x)^(2) meets the curve again at P, then find coordinates of P.

Write the equation of tangent at (1,2) for the curve y=x^(3)+1

If the join of (x_(1),y_(1)) and (x_(2),y_(2)) makes on obtuse angle at (x_(3),y_(3)), then prove than (x_(3)-x_(1))(x_(3)-x_(2))+(y_(3)-y_(1))(y_(3)-y_(2))<0

The length of the tangent of the curve y=x^(3)+2 at (1 3) is