Analytic Geometry Answers

Find the equation of the locus of the center of a moving circle tangent to the y-axis and to a circle with a radius 2 with center at (8, 2).

A point moves so that the angle from the line joining it and the origin to the line (3, -2) and (5, 7) is 45º. Find the equation of the locus.

Find the equation of the locus of the third vertex of a triangle if two of its vertices are (1, -2) and (5, 0) and whose area is 3.

The sum of the distances of a moving point from (3, 0) and (-3, 0) is 8. Find its equation

Find the equation of the locus of a point so that the square of its distance from (3, -3) is always numerically equal to the slope of the line joining it to the same point.

Describe verbally how to solve y mx c = + . What assumptions have you made about the value of m ? 

A highway underpass is parabolic in shape as shown on the diagram below. The curve of the underpass can be modelled by the quadratic function

A highway underpass is parabolic in shape as shown on the diagram below. The curve of the underpass can be modelled by the quadratic function

h(x)=−110x2+95x,

where x and h(x) are in metres. Point D is the highest point of the underpass. Two beams, AB and CD, are inserted to reinforce the curve of the underpass at the top. The length of beam AB is 10,00 m. Determine the length of beam CD to two decimal places.

M​ is​ the​ mid​point​ of​ AC, find​ the​ coordinates​ of​ the​ missing​ end​point

1​ A​(-9,6) and​ M(5, 1)

2​ C​(1,-8) and​ M​ (-8,-4)

Subject : Analytical Dynamics

Find the number of degree of freedom and set of generalized coordinate of the following

1) Rigid body

2) Cylinder rolling down on inclined plane

3) Disk vertically rolling on a plane

4) A particle moving along a curve.