Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Precalculus
Convert equations of conic sections from general to standard form
Which of the following is the equation of the parabola described with vertex at
(
5
,
−
3
)
(5, -3)
(
5
,
−
3
)
, axis parallel to the
y
y
y
-axis and passing through the point
(
1
,
1
)
(1, 1)
(
1
,
1
)
?
\newline
(a)
(
x
−
5
)
2
=
4
(
y
+
3
)
(x - 5)^2 = 4(y + 3)
(
x
−
5
)
2
=
4
(
y
+
3
)
\newline
(b)
(
x
+
5
)
2
=
4
(
y
−
3
)
(x + 5)^2 = 4(y - 3)
(
x
+
5
)
2
=
4
(
y
−
3
)
\newline
(c)
(
y
+
3
)
2
=
4
(
x
−
5
)
(y + 3)^2 = 4(x - 5)
(
y
+
3
)
2
=
4
(
x
−
5
)
\newline
(d)
(
y
−
3
)
2
=
4
(
x
+
5
)
(y - 3)^2 = 4(x + 5)
(
y
−
3
)
2
=
4
(
x
+
5
)
Get tutor help
Write the equation of this conic section in conic form:
x
2
+
4
x
−
4
y
2
−
40
y
=
112
x^{2}+4 x-4 y^{2}-40 y=112
x
2
+
4
x
−
4
y
2
−
40
y
=
112
\newline
This hyperbola opens left/right.
\newline
Plot the foci of the hyperbola, then click next.
\newline
Click to plot points. Click points to delete them.
\newline
Be sure to calculate and try to plot your points as accurately as possible.
Get tutor help
Which type of conic section is defined by the equation
4
x
2
−
16
y
2
+
16
x
−
160
y
−
448
=
0
4 x^{2}-16 y^{2}+16 x-160 y-448=0
4
x
2
−
16
y
2
+
16
x
−
160
y
−
448
=
0
?
\newline
This is an equation of a hyperbola
\newline
Write the equation of this conic section in conic form:
x
2
+
4
x
−
4
y
2
−
40
y
=
112
x^{2}+4 x-4 y^{2}-40 y=112
x
2
+
4
x
−
4
y
2
−
40
y
=
112
\newline
This hyperbola opens
Get tutor help
Write the equation in standard form for the ellipse
x
2
+
8
y
2
=
16
x^2 + 8y^2 = 16
x
2
+
8
y
2
=
16
.
Get tutor help
Write the equation in standard form for the ellipse
x
2
+
7
y
2
=
21
x^2 + 7y^2 = 21
x
2
+
7
y
2
=
21
.
Get tutor help
Express the following in vertex form
\newline
f
(
x
)
=
x
2
+
6
x
−
2
f(x)=x^{2}+6 x-2
f
(
x
)
=
x
2
+
6
x
−
2
Get tutor help
A triangle has side lengths of
(
5.1
g
−
6.9
h
)
(5.1 g-6.9 h)
(
5.1
g
−
6.9
h
)
centimeters,
(
6.4
g
−
8.8
k
)
(6.4 g-8.8 k)
(
6.4
g
−
8.8
k
)
centimeters, and
(
9.3
k
+
3.4
h
)
(9.3 k+3.4 h)
(
9.3
k
+
3.4
h
)
centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
\newline
−
3.5
h
+
0.5
k
+
11.5
g
-3.5 h+0.5 k+11.5 g
−
3.5
h
+
0.5
k
+
11.5
g
\newline
−
1.8
g
h
−
2.4
g
k
+
12.7
h
k
-1.8 g h-2.4 g k+12.7 h k
−
1.8
g
h
−
2.4
g
k
+
12.7
hk
\newline
−
12.3
h
k
+
20.8
g
k
-12.3 h k+20.8 g k
−
12.3
hk
+
20.8
g
k
\newline
−
5.4
k
+
11.5
g
+
2.4
h
-5.4 k+11.5 g+2.4 h
−
5.4
k
+
11.5
g
+
2.4
h
Get tutor help
The graph shows the parabola
y
=
−
(
x
+
4
)
2
+
5
y=-(x+4)^2+5
y
=
−
(
x
+
4
)
2
+
5
. Consider the following linear equation:
y
=
−
3
x
+
b
y=-3x+b
y
=
−
3
x
+
b
for some constant
b
b
b
. If one of the solutions to the system of equations formed by the parabola and the linear equation is
(
−
4
,
5
)
(-4,5)
(
−
4
,
5
)
, which of the following is the other solution?
Get tutor help
y
=
x
2
−
6
(
x
−
1
)
y=x^2-6(x-1)
y
=
x
2
−
6
(
x
−
1
)
Which of the following is an equivalent form of the equation of the graph shown in the
x
y
xy
x
y
-plane, from which the coordinates of vertex
V
V
V
can be identified as constants in the equation?
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
3
x
+
8
y=x^{2}+3 x+8
y
=
x
2
+
3
x
+
8
\newline
Answer:
y
=
y=
y
=
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
9
x
+
1
y=x^{2}+9 x+1
y
=
x
2
+
9
x
+
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
9
x
+
10
y=x^{2}+9 x+10
y
=
x
2
+
9
x
+
10
\newline
Answer:
y
=
y=
y
=
Get tutor help
Write the equation in standard form for the hyperbola
−
x
2
+
4
y
2
−
100
=
0
-x^{2}+4y^{2}-100=0
−
x
2
+
4
y
2
−
100
=
0
.
Get tutor help
A hyperbola centered at the origin has vertices at
(
±
33
,
0
)
( \pm \sqrt{33}, 0)
(
±
33
,
0
)
and foci at
(
±
59
,
0
)
( \pm \sqrt{59}, 0)
(
±
59
,
0
)
.
\newline
Write the equation of this hyperbola.
Get tutor help
A hyperbola centered at the origin has vertices at
(
±
7
,
0
)
( \pm \sqrt{7}, 0)
(
±
7
,
0
)
and foci at
(
±
27
,
0
)
( \pm \sqrt{27}, 0)
(
±
27
,
0
)
.
\newline
Write the equation of this hyperbola.
Get tutor help
(
x
−
7
)
2
+
(
y
+
5
)
2
=
16
(x-7)^{2}+(y+5)^{2}=16
(
x
−
7
)
2
+
(
y
+
5
)
2
=
16
\newline
The given equation represents a circle in the
x
y
x y
x
y
-plane. If
(
x
,
−
5
)
(x,-5)
(
x
,
−
5
)
is a point on the circle, what is a possible value of
x
x
x
?
Get tutor help
(
x
+
4
)
2
+
(
y
+
2
)
2
=
25
(x+4)^{2}+(y+2)^{2}=25
(
x
+
4
)
2
+
(
y
+
2
)
2
=
25
\newline
The given equation represents a circle in the
x
y
x y
x
y
-plane. If
(
−
4
,
y
)
(-4, y)
(
−
4
,
y
)
is a point on the circle and
y
>
0
y>0
y
>
0
, what is the value of
y
y
y
?
Get tutor help
