AA/Precalculus
Name:______________________
Warm-Up
Block:______ Date:__________
Classify/Identify each conic section: (do not put in standard form)
Write Problems #13 in standard form
AA/Precalculus
Unit 2: Conics Day 2
Name:__________________________
Block:_________ Date:____________
Objective: Today we will explore circles. At the end of class, you will be able to identify the graph the
circle, write the equation from a graph of a circle and put the equation in standard form.
A ______________ is formed by cutting a circular cone with a plane perpendicular to the symmetry axis of
the cone. This intersection is a closed curve, and the intersection is parallel to the plane generating the circle of
the cone. A circle is also ____________________________________ that are equally distant from the center.
The equation of a circle is defined as
(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2 ⟺
(𝑥 − ℎ)2 (𝑦 − 𝑘)2
+
=1
𝑟2
𝑟2
where ( h, k ) is the center of the circle and r is the radius.
Example: Graph the circle centered at (3,-2) with radius 4
In standard form, the equation would be
Example: Graphing a Circle in Standard Form:
( x  1)2  ( y  2)2  16
y
Center =
Radius =
x
Practice:
( x  3)2 ( y  4) 2

2
2
2
x  ( y  4)  36
2
2
y
y
Center =
Center =
Radius =
Radius =
x
Writing the Equation of a Circle:
Example:
Write the equation of a circle in standard form with a center at (3, 2) and a radius of 7 cm.
Write the equation of a circle in standard form with a center at (5, 0) and a diameter of 10 cm.
Practice:
Write the equation of a circle in standard form with a center at (2, 7) and a diameter of 14 2 cm.
x
Graphing a Circle in General Form:
y
Example:
Graph the equation x 2  y 2  4 x  6 y  12  0
** Remember, you must change this back into standard form:
x
( x  h)2  ( y  k )2  r 2
Practice:
x2  y 2  2x  4 y  4  0
x2  y 2  6x  2 y  9  0
y
y
x
x
Writing Equations from Circles:
Practice:
Given the graph, write the equation in standard form for the circles below:
Graph the equations below:
Practice
Name:_________________________