Conic Sections : Geometric Representations and Is a a conic section is considered to be a function?

How do I explain how the curves of conic sections can be created geometrically? Can you tell me if a conic section is considered to be a function?

Proofs

1- prove that the diagonals of a rhombus bisect each other at right angels. 2- prove that diagonals of a kite or dart (possibly extended) intersect at right angels. (Note: kite is a convex quadrilateral in which 2 pairs of adjacent sides are congruent dart is a non convex quadrilateral in which 2 pairs of adjacent sides are ...continues

Constructions

1. Show how to constract a triangle given the 3 midpoints of its side. 2. Show how to construct a triangle given the lenght of one side, the size of an adjacent angle and the lenght of the median from that angle.

Constructions

1. Show how to construct a triangle given the length of one side, the distance from an adjacent vertex to the incenter and the radius of the incircle. 2. Show how to construct a triangle ABC given the length of side BC and the altitudes from B and C

Constructions

Show how to construct a triangle given the measure of one angle, the length of the internal bisectore of that angle and the radius of the incircle.

Vectors and analytic geometry

Please find the 1) length and 2) direction (when defined) of 1) A X B and 2) B X A Please show all work, including the grids for the determinants. Thank you. A = 2i - 2j - k B = i - k

Find the cross product and its magnitude of given vectors

Please find the 1) length and 2) direction (when defined) of 1) A X B and 2) B X A Please show all work, including the grids for the determinants. Thank you. A = 2i + 3j B = -i + j

Geometry : Construction of Line Segments

1- Given a unit line segment AB (2 cm) construct a segment of length (1+Sqrt[5])/2 2- Given the unit segment above and construct a segment of length Sqrt[2/3]

Geometry : Construction of a Perpendicular

Given a diameter AB of a circle and a point P as shown in figure construct with straight edge alone a perpendicular from P to AB.

Geometry and Construction : Finding the Hidden Vertex of an Angle

A farmer wishes to erect a striaght fence that will bisect the angle formed by two existing (straight) fences. Unfortunetly, the vertex of the angle is in the middle of a lake. How can we locate the fence line using straight edge and compass? Please see the attached file for the fully formatted problem.