Analytic Geometry Answers

find the coordinates of the point L that divides segment MN into a ratio of ML:LN to 1:3; M(-4,0) and N(0,4). Write your answer in coordinate form (x,y)

Which of the following equations represents an elliptic paraboloid ?

1. "z=y^2"
2. "z=x^2-y^2+2y"
3. "z=x^2+y^2+2x"
4. "z=x^2-y^2+2x"

Use the tetrahedron that has corner coordinates A=(1,-1,0), B=(6,1,3), C= (–3,2,0) and D=(0,6,5) and  check that its centroid will be at (1,2,2).

a)A tetrahedron has 4 corners, 4 faces, 6 edges, and 12 corner angles. How many of our tetrahedron’s 12 corner angles are right angles, and which one(s)?

(b) Determine the projection of the tetrahedron onto the viewing screen when the eye is at (–6,2,2). Colour the side or sides that the viewer can see from this position.

Find the distance between the point and the line/plane 

a. (-1,4);x-3y+2=0

b. (-1,-1,2);2x+5y-6z=4

Write the coordinates for the center of the hyperbola:

((y - 2) ^ 2)/16 - ((x + 1) ^ 2)/144 = 1

Let L be the line given by the vector equation (x,y)=(1,1) + t( sqrt(3),1), t"\\epsilon"R. What is the equation of the image of L after being rotated 15 deg about (1,1) and then translated by vector u=(-1,1)

Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0.

Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0.