1st summative test

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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


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