Analytic Geometry Answers

Does the equation 2/r= 3cos(θ-π/4)+ 2sin(θ+π/4) represent a straight line? Satisfy your answer

What surface is represented by x^2+y^2=9z? Give a rough sketch of it. Obtain the section of this surface by the plane y=0.

Show that the points (2,0,1), (0,4,-3), (-2,5,0) are non-collinear. Hence the equation of plane passing through them.

The projection of the line segment joining (1,2,-1), (4,2,1) on the line x/2=-y=z is 7/2
True or false with correct explanation

A whispering gallery has a semislliptical chilling that is 10m high and 32m. How high is the ceiling above the two foci?

A satellite dish in the shape of paraboloid is 10 ft. across, and 4 ft. deep at its vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to 2 decimal places

Find the magnitude of this vector \\(a= -i+2j +2k\\)

what is the lenght of the conjugate axis?
(x-1)^2/25 -(y+3)^2/9=1

The cables of a suspension bridge are in the shape of parabola. The towers supporting the cables are 800 ft apart and 100 ft high. If cables touch the road surface midway between the towers, what is the hieght of the cable at a point 200 feet from the middles of the bridge?

The section of the conicoid 3x^2-y^2+z^2=1 by the plane y+2z=4 is an ellipse.
True or false with full explanation