Analytic Geometry Answers

Does there pass a plane through the lines (x+4)÷3 =y÷2 =(z−1)÷3 and x÷2 =(y−1)÷1 =(z+1)÷1?

Justify.

Check whether the points (1,−1,−2),(1,−4,2),(3,0,2),(4,−3−2) are coplanar

or not. If they are coplanar, write the equation of the plane they pass through.

Otherwise, change the coordinates of one of the points so that they become

coplanar. In this case, find the plane passing through them.

x^2 +y^2 +z^2 = xyz is the equation of a cone.Is it true or false?

If α,β, γ are direction ratios of a line, then so are α^2 ,β^2, γ^2. Is it true or false ?

Every planar section of an ellipsoid is an ellipse. Is it true or false ?

The circle (x−1)^2 +y^2 = 1,z = 0 lies inside the sphere centred at the origin, andhaving radius 2√2. Is it true or false ?

Show that the closed sphere with centre )7,3,2( and radius 10 in 3 R is contained in the

open cube P = {(x, y,z :) x − 2 <11, y − 3 <11, z − 7 <11}.

Give the equation of a conic which is symmetric to the line x+2 = 0.

Find the nature of the planar section of the conicoid x²/3-y²/4=z by the plane

x+2y−z = 6

Find the equation of the normal to the solid 2x^2 −y^2 +8z^2 = 11 at a point where it

intersects the line x−3 = z =(y+1)÷2.