Analytic Geometry Answers

An archeologist found the remains of an ancient wheel, which she then placed on a grid. If an arc of the wheel passes through A(-7, 0), B(-3, 4) and C(7, 0) locate the center of the wheel, and the standard equation of the circle defining its boundary.

State whether the following statements are true or false. Justify your answer with a brief explanation or with a counter-example.

(a) The curve x4 + y4 = 4a2xy is symmetric with respect to the origin.

(b) The direction cosines of the line x = — y, z=0 are 1/√2, -1/√2,0

(c) The section of 2x² + y²= 2 (1 — z²) by the plane x + 2 = 0 is a hyperbola.-

(d) The xy-plane intersects the sphere

x²+ y² + z² + 2x + 2y — z = 2 in a great circle.

(e) If the projection of a line segment AB on another line is the line segment CD, then

IABI = ICDI•