Q.1
Question
True/False: Determine whether each of the statements that
follow is true or false. If a statement is true, explain why.
If a statement is false, provide a counterexample.
Step-by-Step Solution
Verifieda. True
b. True
c. False
d. True
e. False
f. True
g. False
h. True
A curve created by the intersection of a plane and a circular cone is a cone.
Any plane that does not pass through the vertx will intersect the cone in a curve is called as a conic section.
An ellipse is the set of points in the plane such that the sum of the distances to the foci is constant.
A parabola is the set of points in the plane equidistant from a given fixed line of the parabola and a given fixed point.
A parabola is just a parabola not a hyperbola.
A plane through the vertex will intersect the cone in either a single point , a line.or a pair of intersecting lines.
A hyperbola is the set of points in the plane for which the differences of the distances to the two foci is constant.
It's a parabola because $$r=\frac{1}{1+sin(\theta )}$$ is in standard form. So, when comparing it with standard form e=1. It appears to bea parabola.