The normal to the curve `5x^5-10x^(3)+x+2y+6=0` at the point P(0,-3) meets the curve again at n number of distinct points (other than P then n=

The normal to the curve 5x^(5)-10x^(3)+x+2y+6 =0 at P(0, -3) meets the curve again at the point

Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) meets the curve again at two points.Find the equations of the tangents to the curve at these points.

(i) Find the point on the curve 9y^(2)=x^(3) where normal to the curve has non zero x -intercept and both the x intercept and y- intercept are equal. (ii) If the tangent at (1,1) on y^(2)=x(2-x)^(2) meets the curve again at P, then find coordinates of P (iii) The normal to the curve 5x^(5) -10x^(3) +x+2y+6=0 at the point P(0,-3) is tangent to the curve at some other point (s). Find those point(s)?

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

The equation of the normal to the curve y=x(2-x) at the point (2, 0) is

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.