Transcript 11.1 Intro to Conic Sections & The Circle What is a “Conic Section”? A curve formed by the intersection of a plane.

11.1 Intro to Conic Sections &
The Circle
What is a “Conic Section”?
A curve formed by the intersection of a plane and a double right
circular cone.
Circles : set of all points in a plane at a fixed distance from a fixed point
(center)
(radius)
P(x, y)
r
C(h, k)
Center C(h, k)
Any point on circle P(x, y)
By distance formula:
r 
(x  h)  ( y  k )
2
r  (x  h)  ( y  k )
2
2
2
2
standard form of a circle
Check out the problems around the room. Work together and answer
them all!
1) Find center & radius. x2 + y2 + 8x – 10y = 23
C(–4, 5) r = 8
2) Determine an equation of a circle congruent to the graph of
x2 + y2 = 16 and translated 3 units right and 1 unit down.
(x – 3)2 + (y + 1)2 = 16
3) The general form of a circle is x2 + y2 + Dx + Ey + F = 0.
*In completing the square if r > 0  circle
r = 0  degenerate circle / point circle
r < 1  the empty set (not possible)
Determine what 3x2 + 3y2 – 30x + 18y + 178 = 0 represents.
empty set
4) Determine the equation of the circle that passes through these three
points: (5, 3), (–1, 9), (3, –3).
*Use x2 + y2 + Dx + Ey +F = 0
here’s a hint … for (5, 3): 25 + 9 + 5D + 3E + F = 0
x2 + y2 + 4x – 4y – 42 = 0  (x + 2)2 + (y – 2)2 = 50
5) Determine an equation of a circle that satisfies the center at (2, 3)
tangent to line 5x + 6y = 14.
*remember! Distance from a point to a line
(x1, y1)
d 
A x1  B y 1  C
A B
2
d
Ax + By + C = 0
2
( x  2)  ( y  3) 
2
2
196
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Homework
#1101 Pg 538 #5, 7, 15, 21, 22, 24–26, 30–32, 34,
36, 38, 41, 45, 47, 49, 51