Precalculus General equation of a circle

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Properties of
Circle
Precalculus

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Give the standard equation of the circle
satisfying the given conditions, center (5,-
6), tangent to the x-axis.
EQUATION OF A CIRCLE

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After expanding, the standard equation
(x – 5)2 + (y + 6)2 = 36 can be rewritten as x2 +
y2 - 10x +12y+25 =0, an equation of the circle
in general form.
MORE PROPERTIES OF CIRCLES

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General Form of Equation
If the equation of a circle is given in the general form
Ax2 + By2 + Cx + Dy + E = 0, if A ≠ 0,

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General Form of Equation
Example 1. Identify the center and radius of the circle with the
given equation in each item. Sketch its graph, and indicate the
center.
(a) x2 + y2 - 6x = 7
(b) x2 + y2 -14x + 2y = -14

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Situational Problems Involving
Circles
1. A street with two
lanes, each 10 ft wide,
goes through a
semicircular tunnel with
radius 12 ft. How high is
the tunnel at the edge of
each lane? Round off to 2
decimal places.

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Activity
1. Identify the center and radius
(a) x2+y2=49 (b) x2 + y2-12x-10y = -12
2. A single-lane street 10 ft wide goes through a semicircular
tunnel with radius 9 ft. How high is the tunnel at the edge of
each lane? Round off to 2 decimal places.

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T H A N K YO U
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Reynaldo L. Castro
@reylkastro2
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