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Algebra 2
Write equations of circles in standard form using properties
Write the equation in standard form. Then identify the center and radius.
\newline
14
14
14
.
x
2
+
y
2
−
4
x
−
12
y
−
129
=
0
x^{2}+y^{2}-4 x-12 y-129=0
x
2
+
y
2
−
4
x
−
12
y
−
129
=
0
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A circle in the
x
y
x y
x
y
-plane has its center at
(
−
4
,
5
)
(-4,5)
(
−
4
,
5
)
and the point
(
−
8
,
8
)
(-8,8)
(
−
8
,
8
)
lies on the circle. Which equation represents this circle?
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think of a number he divides the number by
4
4
4
then adds
10
10
10
. the answer is
14
14
14
. write an equation
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(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
(x+3)^{2}+(y-4)^{2}=9
(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
\newline
A circle in the
x
y
x y
x
y
-plane has the equation shown. If the
x
x
x
-coordinate of a point on the circle is
−
3
-3
−
3
, what is a possible corresponding
y
y
y
-coordinate?
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Determine the equation of the circle with radius
138
\sqrt{138}
138
and center
(
−
5
,
0
)
(-5,0)
(
−
5
,
0
)
.
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The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is
3
3
3
.
7
7
7
.
\newline
Which is the principal value of
arctan
(
3.7
)
?
\arctan (3.7) ?
arctan
(
3.7
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
4
-4
−
4
.
98
98
98
\newline
(B)
−
1
-1
−
1
.
83
83
83
\newline
(C)
1
1
1
.
31
31
31
\newline
(D)
4
4
4
.
45
45
45
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The equation of the circle with radius
3
3
3
and centre as the point of intersection of the lines
2
x
+
3
y
=
5
,
2
x
−
y
=
1
2 \mathrm{x}+3 \mathrm{y}=5,2 \mathrm{x}-\mathrm{y}=1
2
x
+
3
y
=
5
,
2
x
−
y
=
1
is
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A circle graphed in the
x
y
xy
x
y
-plane has its center at
(
2
,
3
)
(2,3)
(
2
,
3
)
. If the point
(
8
,
11
)
(8,11)
(
8
,
11
)
lies on the circle, which of the following is an equation of the circle?
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the sector of a circle shown at left has center at
o
o
o
. The radius of the circular sector is
10
10
10
and the area of the sector is
75
75
75
. What is the length of the arc
x
y
z
xyz
x
yz
?
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A circle in the
x
y
xy
x
y
-plane has its center at the point
(
−
6
,
1
)
(-6,1)
(
−
6
,
1
)
. If the point
(
7
,
12
)
(7,12)
(
7
,
12
)
lies on the circle, what is the radius of the circle?
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(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
(x+3)^{2}+(y-4)^{2}=9
(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
\newline
A circle in the
x
y
x y
x
y
-plane has the equation shown. If the
x
x
x
-coordinate of a point on the circle is
−
3
-3
−
3
, what is a possible corresponding
y
y
y
coordinate?
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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
x
2
+
4
x
−
2
y=x^{2}+4 x-2
y
=
x
2
+
4
x
−
2
\newline
Answer:
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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
x
2
+
8
x
+
14
y=x^{2}+8 x+14
y
=
x
2
+
8
x
+
14
\newline
Answer:
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Write the equation in standard form for the circle with radius
2
2
2
centered at the origin.
\newline
______
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