Pre-cal | 1Q Flashcards
A Greek mathematician is said to have studied curves formed by the intersection of a perpendicular plane and a cone.
Menaechmus
intersections would form curves, which became known as..
conic sections
He thoroughly studied the curves formed by the intersection of a plane and a double right circular cone
Apollonius of Perga
the great geometer of the Golden Age of Greek mathematics
Apollonius of Perga
a line lying entirely on the cone
generator of the cone
all generators of a cone pass through the intersection of the two parts
vertex
a curve formed by the intersection of a plane and a double right circular cone
conic section
the four basic type of conics
parabola
ellipse
circle
hyperbola
if the cutting plane is parallel to one and only one generator, the curve is a..
parabola
if the cutting plane is not parallel to any generator, the curve is an..
ellipse
if the cutting plane is not parallel to any generator but is perpendicular to the axis, the ellipse becomes a…
circle
if the cutting plane is parallel to two generators, the curve is a..
hyperbola
the cutting plane does not pass through the certex of the cone
non-degenerate conics
when the cutting plane intersects the vertex of the cone, the resulting cone section is called
degenerate conic
a set of points whose distances from a fixed point are in a constant ratio to their distances from a fixed line that is not passing through the fixed point
conic
fixed point of the conic (F)
focus
the fixed line d corresponding to the focus (d)
directrix
the line that passes through the focus and perpendicular to the directrix (a)
principal axis
the point of intersection of the conic and its principal axis (V)
vertex
the constant ratio (e)
eccentricity
a set of all coplanar points such that the distance from a fixed point is constant
circle
the fixed point of a circle
center of the circle
the constant distances from the center
radius of the circle
a set of coplanar points that are equidistant from a fixed line and a fixed point not on the fixed line
parabola
the fixed line of the parabola
directrix of the parabola
the fixed point of the parabola
focus of the parabola
the line perpendicular to the directrix and passing through the focus F
axis of symmetry
the chord that passes through the focus and perpendicular to the axis of symmetry
latus rectum
the point on the parabola midway between the latus rectum and the directrix
vertex
