Analytic Geometry Answers

The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
True or false with full explanation

The curve x^4+y^4=4a^2xy is symmetric with respect to the origin.
True or false with full explanation

Identify the type of the conic 4(x-2y+1)^2 +9(2x+y+2)^2 = 25

The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
True or false with full explanation

Find the equation of the right circular cone vwhen the straight line 2y+3z=6, x=0 revolves about the z-axis

ABC has vertices at A(3,4), B(-2,0),and C(5,0). Prove the area of the triangle formed by joining the midpoints of ABC is one-quarter the area of ABC:
A) find the distance from the point A(5,7) to the line joining B(-2,1) and C(4,-3)

Find the new equation of the curve (x-2)^2= y(y-1)^2 by the transforming to parallel axes through the point (2,1)

Find the equations of the tangent planes to the conicoid 7x^2-3y^2-z^2+21=0, which pass through the line 7x-6y+9=0, z=3

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.