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Write the equation in standard form for the ellipse with center at the origin, vertex
(
−
10
,
0
)
(-10,0)
(
−
10
,
0
)
, and co-vertex
(
0
,
3
)
(0,3)
(
0
,
3
)
.
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Math Problems
Algebra 2
Write equations of ellipses in standard form using properties
Full solution
Q.
Write the equation in standard form for the ellipse with center at the origin, vertex
(
−
10
,
0
)
(-10,0)
(
−
10
,
0
)
, and co-vertex
(
0
,
3
)
(0,3)
(
0
,
3
)
.
Identify Major Axis:
Vertex is
(
−
10
,
0
)
(-10, 0)
(
−
10
,
0
)
, so the major axis is horizontal and the length of the semi-major axis,
a
a
a
, is
10
10
10
.
\newline
a
=
10
a = 10
a
=
10
Identify Co-vertex:
Co-vertex is
(
0
,
3
)
(0, 3)
(
0
,
3
)
, so the length of the semi-minor axis,
b
b
b
, is
3
3
3
.
\newline
b
=
3
b = 3
b
=
3
Find Center:
The center
(
h
,
k
)
(h, k)
(
h
,
k
)
is at the origin, so
h
=
0
h = 0
h
=
0
and
k
=
0
k = 0
k
=
0
.
Standard Form Equation:
The standard form for a horizontal ellipse is
(
x
−
h
)
2
/
a
2
+
(
y
−
k
)
2
/
b
2
=
1
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
(
x
−
h
)
2
/
a
2
+
(
y
−
k
)
2
/
b
2
=
1
. Plug in
h
=
0
h = 0
h
=
0
,
k
=
0
k = 0
k
=
0
,
a
=
10
a = 10
a
=
10
, and
b
=
3
b = 3
b
=
3
.
(
x
−
0
)
2
/
1
0
2
+
(
y
−
0
)
2
/
3
2
=
1
(x-0)^2/10^2 + (y-0)^2/3^2 = 1
(
x
−
0
)
2
/1
0
2
+
(
y
−
0
)
2
/
3
2
=
1
Simplify Equation:
Simplify the equation.
x
2
100
+
y
2
9
=
1
\frac{x^2}{100} + \frac{y^2}{9} = 1
100
x
2
+
9
y
2
=
1
More problems from Write equations of ellipses in standard form using properties
Question
Write the equation in standard form for the ellipse with center at the origin, vertex
(
−
10
,
0
)
(-10,0)
(
−
10
,
0
)
, and co-vertex
(
0
,
3
)
(0,3)
(
0
,
3
)
.
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Posted 7 months ago
Question
Write the equation in standard form for the ellipse
7
x
2
+
y
2
=
21
7x^2 + y^2 = 21
7
x
2
+
y
2
=
21
.
\newline
______
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Posted 9 months ago
Question
What is the center of the ellipse
x
2
+
2
y
2
−
16
=
0
x^2 + 2y^2 - 16 = 0
x
2
+
2
y
2
−
16
=
0
?
\newline
Write your answer in simplified, rationalized form.
\newline
(
_
_
_
_
_
,
_
_
_
_
_
)
(\_\_\_\_\_,\_\_\_\_\_)
(
_____
,
_____
)
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Posted 7 months ago
Question
What is the length of the major axis of the ellipse
x
2
9
+
y
2
2
=
1
\frac{x^2}{9} + \frac{y^2}{2} = 1
9
x
2
+
2
y
2
=
1
?
\newline
Write your answer in simplified, rationalized form.
\newline
_
_
_
_
_
\_\_\_\_\_
_____
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Posted 7 months ago
Question
What is the center of the ellipse
(
(
x
−
5
)
2
9
)
+
(
(
y
−
2
)
2
54
)
=
1
\left(\frac{(x - 5)^2}{9}\right) + \left(\frac{(y - 2)^2}{54}\right) = 1
(
9
(
x
−
5
)
2
)
+
(
54
(
y
−
2
)
2
)
=
1
?
\newline
Write your answer in simplified, rationalized form.
\newline
(________ , _______)
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Posted 9 months ago
Question
The equation of an ellipse is given below.
\newline
(
x
+
15
)
2
676
+
(
y
−
4
)
2
100
=
1
\frac{(x+15)^{2}}{676}+\frac{(y-4)^{2}}{100}=1
676
(
x
+
15
)
2
+
100
(
y
−
4
)
2
=
1
\newline
What are the foci of this ellipse?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
−
15
+
24
,
4
)
(-15+\sqrt{24}, 4)
(
−
15
+
24
,
4
)
and
(
−
15
−
24
,
4
)
(-15-\sqrt{24}, 4)
(
−
15
−
24
,
4
)
\newline
(B)
(
−
15
,
4
+
24
)
(-15,4+\sqrt{24})
(
−
15
,
4
+
24
)
and
(
−
15
,
4
−
24
)
(-15,4-\sqrt{24})
(
−
15
,
4
−
24
)
\newline
(C)
(
−
39
,
4
)
(-39,4)
(
−
39
,
4
)
and
(
9
,
4
)
(9,4)
(
9
,
4
)
\newline
(D)
(
−
15
,
28
)
(-15,28)
(
−
15
,
28
)
and
(
−
15
,
−
20
)
(-15,-20)
(
−
15
,
−
20
)
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Posted 9 months ago
Question
The equation of an ellipse is given below.
\newline
(
x
−
5
)
2
3
+
(
y
−
7
)
2
6
=
1
\frac{(x-5)^{2}}{3}+\frac{(y-7)^{2}}{6}=1
3
(
x
−
5
)
2
+
6
(
y
−
7
)
2
=
1
\newline
What are the foci of this ellipse?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
5
,
7
+
3
)
(5,7+\sqrt{3})
(
5
,
7
+
3
)
and
(
5
,
7
−
3
)
(5,7-\sqrt{3})
(
5
,
7
−
3
)
\newline
(B)
(
−
5
,
−
7
+
3
)
(-5,-7+\sqrt{3})
(
−
5
,
−
7
+
3
)
and
(
−
5
,
−
7
−
3
)
(-5,-7-\sqrt{3})
(
−
5
,
−
7
−
3
)
\newline
(C)
(
−
5
+
3
,
−
7
)
(-5+\sqrt{3},-7)
(
−
5
+
3
,
−
7
)
and
(
−
5
−
3
,
−
7
)
(-5-\sqrt{3},-7)
(
−
5
−
3
,
−
7
)
\newline
(D)
(
5
+
3
,
7
)
(5+\sqrt{3}, 7)
(
5
+
3
,
7
)
and
(
5
−
3
,
7
)
(5-\sqrt{3}, 7)
(
5
−
3
,
7
)
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Posted 9 months ago
Question
The equation of an ellipse is given below.
\newline
x
2
46
+
(
y
+
8
)
2
26
=
1
\frac{x^{2}}{46}+\frac{(y+8)^{2}}{26}=1
46
x
2
+
26
(
y
+
8
)
2
=
1
\newline
What are the foci of this ellipse?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
0
+
20
,
8
)
(0+\sqrt{20}, 8)
(
0
+
20
,
8
)
and
(
0
−
20
,
8
)
(0-\sqrt{20}, 8)
(
0
−
20
,
8
)
\newline
(B)
(
0
,
8
+
20
)
(0,8+\sqrt{20})
(
0
,
8
+
20
)
and
(
0
,
8
−
20
)
(0,8-\sqrt{20})
(
0
,
8
−
20
)
\newline
(C)
(
0
,
−
8
+
20
)
(0,-8+\sqrt{20})
(
0
,
−
8
+
20
)
and
(
0
,
−
8
−
20
)
(0,-8-\sqrt{20})
(
0
,
−
8
−
20
)
\newline
(D)
(
0
+
20
,
−
8
)
(0+\sqrt{20},-8)
(
0
+
20
,
−
8
)
and
(
0
−
20
,
−
8
)
(0-\sqrt{20},-8)
(
0
−
20
,
−
8
)
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Posted 9 months ago
Question
Write an equation for an ellipse centered at the origin, which has foci at
(
±
12
,
0
)
( \pm 12,0)
(
±
12
,
0
)
and vertices at
(
±
13
,
0
)
( \pm 13,0)
(
±
13
,
0
)
.
Get tutor help
Posted 9 months ago
Question
Write an equation for an ellipse centered at the origin, which has foci at
(
0
,
±
6
)
(0, \pm 6)
(
0
,
±
6
)
and vertices at
(
0
,
±
37
)
(0, \pm \sqrt{37})
(
0
,
±
37
)
.
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Posted 9 months ago
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