# Analytical Geometry

The equation of the circle is given as:

x^2+y^2=25

A parallelogram is constructed as follows:

Vertex O is at the origin, vertex A is on the circle, vertex C is on the y-axis and the diagonal AC is parallel to the x-axis.

See attached figure

Question:

1. Find the locus of vertex B.

2. Describe the geometrical shape that is described by the equation you found in part 1, and find its intersection points with the axis.

https://brainmass.com/math/analytic-geometry/analytical-geometry-locus-vertex-21189

#### Solution Preview

Please see the attached files.

The equation of the circle is given as:

A parallelogram is constructed as follows:

Vertex O is at the origin, vertex A is on the circle, vertex C is on the y-axis and the diagonal AC is parallel to the ...

#### Solution Summary

The solution shows how to extract geometrical information using analytical equations, mainly showing how o identify a shape from its equation.