What is the shape of path followed by the projectile? Show the path of projectile is Parabola.

A projectile is an object projected into air with a velocity V so that it is moving under the influence of gravity. a)What is the shape of the path of projectile? b)As a projectile moves in its path,is there any point along the path where the velocity and acceleration vectors are perpendicular to each other. c)If E is energy with a projectile is projected, (i)What is the kinetic energy at the highest point. (ii)What is P.E at highest point?

A body is projected into air at an angle theta with the horizontal. a)What is the trajectory followed by this projectile? (i) Ellipse,(ii)Parabola,(iii)Straight line,(iv)Circle. b)Give a mathematical proof for your answer. c)Trajectory of a body in a projectile motion is given by y=x-(x^2/80) . x and y are in meters.Find maximum height of this projectile.