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Algebra 2
Write equations of circles in standard form using properties
A circle has a radius of
5
3
\dfrac{5}3
3
5
units and is centered at
(
9.2
,
−
7.4
)
(9.2,-7.4)
(
9.2
,
−
7.4
)
. Write the equation of this circle.
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A circle in the
x
y
xy
x
y
-plane has its center at
(
h
,
k
)
(h, k)
(
h
,
k
)
and radius
r
r
r
. What is an equation of the circle?
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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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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 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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