Download Unit 13 Day 1 - Conic Sections and Circles

Unit 13 Day 1 - Conic Sections
We will review what Conic Sections
are
and
I will write the equations for
circles in both general and standard
form.
April 26, 2017
Cones
 A cone is created from two
nonperpendicular lines
intersecting at a point V.
 If one line is fixed (the
axis) and the other one
rotates around this axis
(the generator) it creates a
right circular cone with
vertex V.
Definition of a conic section:
 A conic section is the intersection of
a plane and a cone.
 By changing the angle and the location
of intersection, a parabola, circle,
ellipse or hyperbola is produced.
Circle
Circle - when
a plane
intersects a
double-napped
cone and is
parallel to the
base of a cone.
Parabola
Parabola -
when a plane
intersects a
double-napped
cone and is
parallel to the
side of the cone.
Ellipse
 Ellipse - when a plane
intersects a doublenapped cone and is
neither parallel nor
perpendicular to the
base of the cone.
 The figure is a closed
curve.
 It only intersects one
nappe of the cone.
Hyperbola
Hyperbola - when a
plane intersects
both nappes of a
double-napped cone.
The figure consists
of two open curves.
Circles
(h, k)
r
• all points equidistant (radius) from
one point (center).
Circles (flipbook)
The standard form of the equation
of a circle with center C(h,k) and
radius r is:
(x  h)  (y  k)  r
2
2
General Form of Circle
2
x
+
2
y
2
+ Dx + Ey + F = 0
Determine the center and radius of
the circle with the given equation.
Graph it by hand.
(x + 1)2 + (y – 3)2 = 16
Center (-1,3)
radius = 4
Write the general form of the
equation.
(x + 1)2 + (y – 3)2 = 12
x2 + 2x + 1 + y2 – 6y + 9 = 12
x2 + y2 + 2x – 6y – 2 = 0