On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 m when it is 6 m away from the point of projection. Finally it reaches the ground 12 m away from the starting point. Find the angle of projection.

Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find an equation of it.

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x²−2x+8y+17= 0

Find the vertex, focus, equation of directrix and length of the latus rectum of the following: y²−4y−8x+12 = 0

Identify the type of conic and find centre, foci, vertices, and directrices of each of the following :
18x²+12y²−144x+48y+120 = 0