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.

Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) intersects the curve again in two points. Also find these points.

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=

(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 4x^(3)=27y^(2) at the point (3,2) meets the curve again at the point (a,b) . Then |a|+|b| is equal to -

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

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot