The parametric equations of a curve are given by `x-sec^(2)t, y=cot t`.If the tangent at `P(t=(pi)/(4))` meets the curve again at Q, then show that, `PQ=(3sqrt(5))/(2)`.

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P .

A curve is given by the equation x=sec^(2)theta,y=cottheta. If the tangent at P where theta=pi//4 meets the curve again at Q, the [PQ] is where [.] represents the greatest integer function, "______"

The parametric equation of a parabola is x=t^2-1,y=3t+1. Then find the equation of the directrix.

The parametric equation of a parabola is x=t^2+1,y=2t+1. Then find the equation of the directrix.

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

A curve is represented by the equations x=sec^2ta n dy=cott , where t is a parameter. If the tangent at the point P on the curve where t=pi/4 meets the curve again at the point Q , then |P Q| is equal to (5sqrt(3))/2 (b) (5sqrt(5))/2 (c) (2sqrt(5))/3 (d) (3sqrt(5))/2

Find the equation of tangent to the curve given by x = a sin^(3) t , y = b cos^(3) t at a point where t = (pi)/(2) .

The parametric equation of a curve is given by, x=a(cos t+log tan(t/2)) , y=a sin t. Prove that the portion of its tangent between the point of contact and the x-axis is of constant length.

Find the equation of the tangents and normal to the curve x= sin 3t, y= cos 2t " at " t=(pi)/(4)