Analytic Geometry Answers

A parabolic reflector has a diameter of 20cm and it's depth is 5cm. Find the focus show solution and graph

(1) a) Give parametric equation (point-direction form) of the line which lies on both of the planes: x+y+z= 1 and -x+2y + 10z 2. What is the direction d of this line? b) Let ny and n₂ be the normal vectors to the two given planes. Without actual computation, describe the relationship between d and n₁ x n₂.

The strings of a horizontal suspension are supporter by two towers 100 feet apart and 25 feet high. Find the parabolic equation (in standard form) with the center of the bridge as the origin. Note: A suspension bridge cable hangs in a parabolic arc when the weight is evenly distributed along horizontal line.

Find an equation for the plane that passes through the point (-7,10,8), is parallel to the line x= 6−t, y= 9 +t, z=−5+ 2t,and intersects the plane 2x+y−z=e^pi^sqrt2at a 30◦angle.

The abiscissa of a point in the 4th quadrant is numerically three times its ordinate and is 10 units from (-2,4). Find the point.

a) Give parametric equation (point-direction form) of the line which lies on both of the planes:

x + y + z = 1 and −x + 2y + 10z = 2. What is the direction d of this line?

b) Let n1 and n2 be the normal vectors to the two given planes. Without actual computation,

describe the relationship between d and n1 × n2.

Let P QR be a triangle with coordinates P = (x1, y1, z1), Q = (x2, y2, z2) and R = (x3, y3, z3).

a) Prove that the triangle P QR lies on a plane. Find the equation of this plane.

b) Let (x, y, z) be a point in the plane containing the triangle. Prove that the det

x − x1 y − y1 z − z1

x − x2 y − y2 z − z2

x − x3 y − y3 z − z3

= 0.

Give parametric equation (point-direction form) of the line which lies on both of the planes:

x + y + z = 1 and −x + 2y + 10z = 2. What is the direction d of this line?

b) Let n1 and n2 be the normal vectors to the two given planes. Without actual computation,

describe the relationship between d and n1 × n2.

a) Give parametric equation (point-direction form) of the line which lies on both of the planes:

x + y + z = 1 and d x + 2y + 10z = 2. What is the direction d of this line?

b) Let n1 and n2 be the normal vectors to the two given planes. Without actual computation,

describe the relationship between d and n1 × n2.

Let P QR be a triangle with coordinates P = (x1, y1, z1), Q = (x2, y2, z2) and R = (x3, y3, z3).

a) Prove that the triangle P QR lies on a plane. Find the equation of this plane.

b) Let (x, y, z) be a point in the plane containing the triangle. Prove that the det

x − x1 y − y1 z − z1

x − x2 y − y2 z − z2

x − x3 y − y3 z − z3

= 0.