That's true. The qualifying phrase "no matter the shape" is meaningless ... the shape
has already been completely specified by the earlier part of the question.
Yes, it is true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
yes
Yes - it always has exactly two parallel sides.
If the equation of the parabola is represented byy = ax^2 + bx + c then it crosses the x-axis twice if and only if b^2 > 4ac
True
True.
Yes, it is true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
It is the bisector of any 2 parallel chords drawn to the parabola. It is always parallel to the axis of the parabola.
Yes, a transversal line always intersects two parallel lines.
Yes, a parabola always has a vertex. However, it may not always have roots. The roots of a parabola are the x-values where the parabola intersects the x-axis. It is possible for a parabola to have two, one, or no roots depending on the discriminant of the quadratic equation.
yes because they will always equal 180 degrees, regardless of the angle at which the transversal intersects the two parallel lines
No, but any parabola can be transformed into the form y = x^2.
Yes, it is.
yes
momentum is product of moment of inertia and angular velocity. There is always a 90 degree phase difference between velocity and acceleration vector in circular motion therefore angular momentum and acceleration can never be parallel
An equation for a parabola always has some type of irregular variable, usually a squared variable or higher.