2. Conics section
Circle – when the plane is horizontal
Parabola – when the plane intersects only one cone to from an unbounded curved.
Ellipse – when the (tilted) plane intersects only one cone to form a bounded curve.
Hyperbola – when the plane (not necessarily vertical) intersects both cones to form
two unbounded curves (each called a branch of the hyperbola)
3. The Definition of Circle
A circle is the set of all points in the plane that are
equidistant from a fixed pointcalled the center of the
circle. The fixed point is the center of a circle and
the fixed distance is the radius. The distance
between the center and any point on the circle is the
radius. A circle may also be considered a special kind
of ellipse (for the special case when the tilted plane
is horizontal).
4. Identifying the Center and the Radius of a Circle
(General Form)
(Standard Form)
(h,k) Center of the Circle
( r ) Radius
5. Identify the center and radius of the circle with the given equation in each item. Sketch its graph,
and indicate the center.
1. x2+y2-6x=7 (b/2
x2-6x+9+ =7+9 = (6/2
(x-3+ =16 =(3
x=3 y=0 =9
(h,k)= (3,0) r=4
Solution: The first step is to rewrite each equation in standard form by completing the
square in x and in y. from the standard equation; we can determine the center and radius
(𝟑,𝟎)
PST
