Analytic Geometry Answers

The line x=y=z-1 intersects the cone x^2+y^2+z^2+2yz+2zx+2xy=0 at exactly one point

Find the semi vertical angle of a cone with axis x/1=y/2=z/3 and x-axis is the generator?

find the equation of the straight line that passes through the intersection point between the lines x + y = 3 and 2x - 3y = 16 and perpendicular to the straight line y = 4x - 3

Give the equation of two planes that meet at 90°

The line x=y=z-1 intersects the cone x^2+y^2+z^2+2yz+2zx+2xy=0 at exactly one point.
True or false with correct explanation

Find the equation of the cone whose vertex is at the origin and base is the circle x=a, y^2+z^2=b^2.

Find the equation of the cylinder whose base is the circle x^2 + y^2=4 , x+y+2z=3

Find the area of triangle determinied by the point P(-3,1-1) Q(-2,0,5) and R(-4,-1,2).

Determine the equation of the line perpendicular to 3y + 4x = 1 and passing through the point A (-1, 4)

The line x+1=1-y=-5z lies in the plane 2x +3y -5z =1.
True or false with full explanation