[" 4.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_(1)y_(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)

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 .

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again at (x_(2),y_(2)) , then (x_(2))/(x_(1))+(y_(2))/(y_(1)) is equal to

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))+(y2)/(y_(1))=-1

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 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 (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 to the curve x^(3)+y^(3)=a^(3) at the point (x_(1),y_(1)) intersects the curve again at the point (x_(2),y_(2)) , then show that, (x_(2))/(x_(1))+(y_(2))/(y_(1))+1=0 .

If the points (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)) are collinear show that (y_(2)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0