9­1 Notes.notebook
April 06, 2015
9.1 Circles and Parabolas
conic section ‐ intersection of a plane and a double‐napped cone
(p.660 pictures)
circle: (x‐h)2+(y‐k)2=r2 center: (h,k) radius: r
parabola: y = 4p(x‐h)2+k
or
(y‐k)2=4p(x‐h)
vertex: (h,k)
ellipse: (x‐h)2 + (y‐k)2 = 1
a2
b2
hyperbola: (x‐h)2 ‐ (y‐k)2 = 1
a2
b2
Apr 2­8:06 AM
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9­1 Notes.notebook
April 06, 2015
Definition of Circle ­ A circle is the set of all points (x,y) in a plane that are equidistant from a fixed point (h,k) called the center of the circle. The distance r between the center and any point (x,y) on the circle is the radius.
The standard form of the equation of a circle is:
(x­h)2 + (y­k)2 = r2
The point (h,k) is the center of the circle, and the positive number r is the radius of the circle. The standard form of the equation of a circle whose center is the origin, (h,k) is:
x2 + y2 = r2
Ex.1 The point (1,4) is on a circle whose center is at (­2,­3). Write the standard form of the equation of the circle.
Apr 2­8:08 AM
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9­1 Notes.notebook
April 06, 2015
Ex. 2 Sketch the circle given by the equation x2 ­ 6x + y2 ­ 2y + 6 = 0 and identify its center and radius.
Ex.3 Find the x­ and y­intercepts of the graph of the circle given by the equation
(x­4)2 + (y­2)2 = 16
Apr 2­8:16 AM
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9­1 Notes.notebook
April 06, 2015
19.
Apr 13­10:51 AM
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9­1 Notes.notebook
April 06, 2015
ASSN: p. 667­669 1­11 odd 17­23 odd, 29
Apr 2­8:39 AM
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