Tangent is drawn to `y=x^3` at `P(t,t^3)` , it intersects curve again at Q.Find ordinate of point which divide PQ internally in 1:2

If the tangent to the curve y=x^(3) at the point P(t,t^(3)) meets the curve again at Q , then the ordinate of the point which divides PQ internally in the ratio 1:2 is

Tangent at (2,8) on the curve y=x^(3) meets the curve again at Q.Find the coordinates of Q .

Tangent at P(2,8) on the curve y=x^(3) meets the curve again at Q.Find coordinates of Q.

Tangent at P(2,8) on the curve y=x^(3) meets the curve again at Q. Find coordinates of Q.

If P-=(2,-1,4),Q-=(3,2,1) then the co-ordinates of the point which divides PQ externally in the ratio 2:1 are

The tangent to the curve y=x^(3) at the point P(t, t^(3)) cuts the curve again at point Q. Then, the coordinates of Q are

The tangent to the curve y=x-x^(3) at a point P meets the curve again at Q. Prove that one point of trisection of PQ lies on the Y-axis. Find the locus of the other points of trisection.

If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

if the tangent to the parabola y=x(2-x) at the point (1,1) intersects the parabola at P. find the co-ordinate of P.

Tangents drawn to the parabola y^(2)=8x at the points P(t_(1)) and Q(t_(2)) intersect at a point T and normals at P and Q intersect at a point R such that t_(1) and t_(2) are the roots of equation t^(2)+at+2=0;|a|>2sqrt(2) then locus of R is