If the tangent at the point `(at^2, at^3)` on the curve `ay^2 = x^3` meets the curve again at:

If the tangent at the point (a,b) on the curve x^(3)+y^(3)=a^(3)+b^(3) meets the curve again at the point (p,q) then show that bp+aq+ab=0

If the tangent at the point (p,q) to the curve x^(3)+y^(2)=k meets the curve again at the point (a,b), then

If the tangent at (16,64) on the curve y^(2) = x^(3) meets the curve again at Q(u, v) then uv is equal to_____

The tangent at (t,t^(2)-t^(3)) on the curve y=x^(2)-x^(3) meets the curve again at Q, then abscissa of Q must be

Tangent at a point P_(1) [other than (0,0)] on the curve y=x^(3) meets the curve again at P_(2). The tangent at P_(2) meets the curve again at P_(3) and so on. The ratio of area of DeltaP_(1)P_(2)P_(3) to that of DeltaP_(2)P_(3)P_(4) is

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

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

Tangent at a point P_1\ (ot h e r\ t h a n\ (0,0) on the curve y=x^3 meets the curve again at P_2dot The tangent at P_2 meets the curve again at P_3 and so on. Show that the abscissae of P_1,\ P_2,\ P_n form a G P . Also find the ratio (a r e a\ ( P_1P_2P_3))/(a r e a\ ( P_2P_3P_4))dot