Analytic Geometry Answers

Find co-ordinates of the points on the line (x+2)/3= (y+1)/2= (z-3)/2 at a distance 3√2 from the point (1, 2, 3).

Trace the conicoid given by x^2+2z^2=4y What are the sections of this conicoid by the planes x+2=0 and y=1 Describe geometrically.

Find the vertices, eccentricity, foci and asymptotes of the hyperbola.
Also trace it. Under what conditions on the line x^2/8-y^2/4=1 will be tangent
to this hyperbola? Explain geometrically.

Obtain the equation of the plane passing through the line x-2/2=-(y+1)/1 z-3/4 and
which is perpendicular to the plane x+2y+z=4

Find the distance of the line obtained in part (a), from the origin by expressing it in the normal form. Also find the intercepts made by this line on the coordinate axes.

Find the equation of the pline which passes through (1,root3) and makes an angle 30 with the line x-root3y+root3=0

Find the equation of the plane which passes through the line of intersection of the planes 2x+y-2z=6 and makes equal angles with 2x+3y+6z=5 these planes.

Find the angle between the lines x=1 z-y=0 and 2x-y=-1,z=1

For what value(s) of α, the conicoid x^2+y^2+az^2+2yz +xy+2y+z+3=0 has a unique centre? Give reason for your answer.

Find the equation of the cylinder with base curve x^2+y^2+z^2-2x-4z+1=0,2X+y+z=2