Analytic Geometry Answers

Graph the ellipse with equation x squared divided by forty nine plus y squared divided by thirty six = 1

Let R be the point which divides the line segment joining P(2,1,0) and Q(-1,3,4) in the ratio 1:2 such that PR<PQ. Find the =n of the line passing through R and parallel to the line x/2=y/1=z/3

Find two unit vectors perpendicular to both A = ˆi − 2ˆj + 3kˆ
r
and B = −2ˆi + 4ˆj
r
.

Find the angel between the x-axis and the tangent to the hyperbola xy=9 at(3,3)

Find the path traced by the centre of the sphere which touches the lines
x/y = y/(-1) = z/2 and 2x = y , y-z = 0.

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