Which of the following points lie on the parabola `x^2=4a y ?` a.`x=a t^2, y=2a t` b. `x=2a t ,\ y=a t^2` c. `x=2a t^2, y=a t` d. `x=2a t ,\ y=a t^2`

Find the equation of the tangent to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

Find the equation of the tangent and normal to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

Find the equation of the tangent and normal to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

The length of the chord intercepted on the line 2x-y+2=0 by the parabola x^(2)=8y is t then t=

Find y_2 in each of the following cases: y=t^2+t^3 , x=t-t^4

Which of the following curves in the x -y plane cuts every straight line in the plane? (1) x=t,y=t^(2) and (2)x=t,y=t^(3) and (3) x=t^(2),y=t^(3) and x=t^(3),y=t^(5)

The locus of the moving point whose coordinates are given by (e^t+e^(-t),e^t-e^(-t)) where t is a parameter, is x y=1 (b) x+y=2 x^2-y^2=4 (d) x^2-y^2=2

The locus of the moving point whose coordinates are given by (e^t+e^(-t),e^t-e^(-t)) where t is a parameter, is x y=1 (b) x+y=2 x^2-y^2=4 (d) x^2-y^2=2