1st summative test
The collection of all such points forms a shape called
parabola
When the plane is tilted further so that it is parallel to one and only one generator and intersects only one nappe of the cone, a /an(3) ____________ is formed.
parabola
is the set of all points in a plane equidistant from a fixed point and a fixed line.
parabola
the plane is parallel to a generator line of the cone
parabola
how to sketch a hyperbola
sketch the central box, asymptotes, plot the vertices and sketch the hyperbola
This equation can be converted into standard form using completing of (13) _______.
square in both variables
The segment V1V2 is called the__. Its length is
transverse axis. 2a
If the coefficient of the linear (non-squared) part is positive, the parabola opens
upward or to the right
is the point midway between the focus and the directrix.
vertex
If the x-part is squared, the parabola is
vertical
in the standard equation of ellipse, if the y-part has the bigger denominator, the ellipse is
vertical
We collect here the features of the graph of a parabola with standard equation
x2 = 4cy or x2 = −4cy, where c > 0.
. The standard equation of a circle is
x^2+y^2=r^2
However, when the circle has a center at origin: C(0,0), the standard equation would be (11)__________.
x^2+y^2=r^2
. is it a misconception that each branch of hyperbola is a parabola.
yes
does parabolas and hyperbolas have very different features?
yes
The points__ and __ are called the foci of the hyperbola.
F1 and F2
the common distance
radius
Hyperbolas can be used in so-called
"trilateration", or positioning problems
The graph of the equation is a parabola with focus F(__,__) and directrix y=____. So the graph of is a parabola with focus F(__,__) and directrix y=_____.
(0,c) y=-c (0,3) y=-3
To graph the equation of the circle into the coordinate plane, use the center represented by (14) _____. After locating the center, use the value of the (15)_______ to move in all directions and then connect the dots to form a circle
(h,k) radius
This is the standard equation of the circle with center ()and radius()
(h,k)(r)
Given a general equation of the conic sections, we can determine what type of conics by collecting the values (4)___, (5)___ and (6)___.
A,B,C
The __ of the hyperbola are two lines passing through the center which serve as a guide in graphing the hyperbola
asymptotes
This line divides the parabola into two parts which are mirror images of each other.
axis of symmetry
The point C is called the
center
The first type of conic section is circle. It is defined as a set of all points in a plane equidistant from a fixed point called (7)_______ of the circle and the constant equal distance is called (8)________.
center, radius
The set of all points P having the same distance from C is called a
circle
When the plane is perpendicular to the axis of the cone and intersects each generator, a/an (1).__________is formed.
circle
is a special case of ellipse in which the plane is perpendicular to the axis of the cone.
circle
4 types of conic sections
circle,parabola,ellipse,hyperbola
is a curved formed by a plane passing through a double-napped circular cone.
conic sections
he absolute value of the difference of each of the distances from F1 and F2 to (x,y) is
d
A hyperbola is the set of all points in the plane for which the ________ of the distances from two fixed points F1 and F2 is constant
difference
If the coefficient of the linear (non-squared) part is negative, the parabola opens
downward or to the left.
However, when the plane is tilted slightly so that it intersects each generator, but only intersects one nappe of the cone, a/an (2)___________ is formed.
ellipse
when the (tilted) plane intersects only one cone to form a bounded curve
ellipse
The points F1 and F2 are called the _______ of the hyperbola.
foci
are c units above and below, respectively, the origin.
focus and directrix
A parabola is the set of all points in the plane that are equidistant from a fixed point called the _________ and fixed line called the __________ of the parabola.
focus, directrix
The point F is its and the line ℓ its
focus, directrix
This equation of the circle Ax2 + By2 + Cx + Dy + E = 0, is called (12)_____________________.
general form
If the parabola opens downward, the vertex is the
highest point
; if the y-part is squared, the parabola is
horizontal
in the standard equation of ellipse, if the x-part has the bigger denominator, the ellipse is
horzontal
It is possible to locate the place from which a sound, such as gunfire, emanates. Long Range Aid to Navigation (LORAN for short) system, of ship or aircraft
hyperbola
is generated when plane intersects both nappes.
hyperbola
is the set of all points (x,y) in the plane
hyperbola
the intersection is an unbounded curve and the plane is not parallel to a generator line of the cone and the plane intersects both halves of the cone.
hyperbola
If the parabola opens upward, the vertex is the
lowest point