If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka

## Decimal to Fraction

• Given: A decimal (positive decimals only)
To Convert: to a simplified fraction
• $=$

# Conic Sections Calculators

### Calculators for Circles

All input values should be integers or decimals only. No fractions.
Some of the output values are in fractions and/or radicals. Pick the one you need.
Simplify further as necessary.

• Given: Standard Form of the Equation of a Circle
To Find: other details

$(x - $$)^2 \:\:+\:\: (y -$$)^2$ $\:\:=\:\:$ $^2$

The center is (, )

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

• Given: General Form of the Equation of a Circle
To Find: other details

$x^2$ $+$ $y^2$ $+$ $x$ $+$ $y$ $+$ $= 0$

The center is (, )
OR
(, )

The Standard Form is:
$(x - $$)^2 \:\:+\:\: (y -$$)^2$ $\:\:=\:\:$
$^2$

• Given: Center, Radius of a Circle
To Find: other details

The center is (, )

The Standard Form is:
$(x - $$)^2 \:\:+\:\: (y -$$)^2$ $\:\:=\:\:$
$^2$

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

• Given: Center, Tangent to a Line
To Find: other details

The center is ( , )

For a circle that is tangent to the x-axis, set y = 0
For a circle that is tangent to the y-axis, set x = 0

The diameter is

The Standard Form is:
$(x -$ $)^2$ $\:\:+\:\:$
$(y -$ $)^2$ $\:\:=\:\:$
$^2$

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

• Given: Any Two Points
To Find: Point on the $y-axis$ Equidistant from the Two Points

1st point is (, )

2nd point is (, )

The point on the $y-axis$ equidistant from the two points is
(, )

• Given: Any Two Points
To Find: Point on the $x-axis$ Equidistant from the Two Points

1st point is (, )

2nd point is (, )

The point on the $x-axis$ equidistant from the two points is
(, )

• Given: Endpoints of the Diameter of a Circle
To Find: other details

1st endpoint of diameter is (, )

2nd endpoint of diameter is (, )

The center is (, )
OR
(, )

The diameter is OR

The Standard Form is:
$(x - $$)^2 \:\:+\:\: (y -$$)^2$ $\:\:=\:\:$
$^2$

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

• Given: Center, Point on the Circumference of a Circle
To Find: other details

The center is (, )

1st endpoint of diameter is (, )

The diameter is OR

2nd endpoint of diameter is (, )

The Standard Form is:
$(x - $$)^2 \:\:+\:\: (y -$$)^2$ $\:\:=\:\:$
$^2$

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

• Given: Center, Radius of a Circle; a Point
To Determine: if the Point Lies on the Circle

The center is ( , )

Point is ( , )

The point:

• Given: Center, Point on the Circumference of a Circle, Another Point
To Find: the Radius and to determine if the Other Point Lies on the Circle

The center is ( , )

1st endpoint on the cirle is ( , )

2nd point is ( , )

The 2nd point:

• Given: Any Three Points on the Circumference of A Circle
To Find: other details

Point 1 = ( , )

Point 2 = ( , )

Point 3 = ( , )

The center is
( , )

The diameter is

The Standard Form is:
$(x -$ $)^2$ $\:\:+\:\:$
$(y -$ $)^2$ $\:\:=\:\:$
$^2$

The General Form is:
$x^2$ $+$ $y^2$ $+$
$x$ $+$ $y$ $+$
$= 0$

### Calculators for Ellipses

All input values should be integers or decimals only. No fractions.
Some of the output values are in fractions and/or radicals. Pick the one you need.
Simplify further as necessary.

• Given: Standard Form of the Equation of an Ellipse
Center is at the origin (0, 0)
Denominator is a result of squaring
To Find: other details
 $x^2$ $y^2$ $+$ $=\;\;\;\;\;1$

Horizontal distance from the center to the boundary =

Vertical distance from the center to the boundary =

The major axis is the

The minor axis is the

The ellipse is a ellipse

Length of the major axis =

Length of the minor axis =

Center = ( , )

Endpoints of the major axis (Vertices) =
( , )
and
( , )

Endpoints of the minor axis =
( , )
and
( , )

Foci =
( , )
and
( , )

Linear Eccentricity (distance from the center to either focus) =

Distance between the foci =

Eccentricity =

Area =

Length of the Latus Rectum =

Endpoints of the Latus Rectum passing through one focus =
( , )
and
( , )
Endpoints of the Latus Rectum passing through the other focus =
( , )
and
( , )

Distance between the two Directrixes =

The two Directrixes are

and

The Factored Form is:
($x -$ )$^2\;\;+$
($y -$ )$^2\;\;=$

The General Form is:
$x^2\;\;\;+\;\;\;$ $y^2\;\;\;+\;\;\;$
$x\;\;\;+\;\;\;$ $y\;\;\;+\;\;\;$
$=\;0$

Perimeter ≈

• Given: Standard Form of the Equation of an Ellipse
Center is at the origin (0, 0)
Denominator is squared
To Find: other details
 $x^2$ $y^2$ $+$ $=\;\;\;\;\;1$ $^2$ $^2$

Horizontal distance from the center to the boundary =

Vertical distance from the center to the boundary =

The major axis is the

The minor axis is the

The ellipse is a ellipse

Length of the major axis =

Length of the minor axis =

Center = ( , )

Endpoints of the major axis (Vertices) =
( , )
and
( , )

Endpoints of the minor axis =
( , )
and
( , )

Foci =
( , )
and
( , )

Linear Eccentricity (distance from the center to either focus) =

Distance between the foci =

Eccentricity =

Area =

Length of the Latus Rectum =

Endpoints of the Latus Rectum passing through one focus =
( , )
and
( , )
Endpoints of the Latus Rectum passing through the other focus =
( , )
and
( , )

Distance between the two Directrixes =

The two Directrixes are

and

The Factored Form is:
($x -$ )$\;^2\;\;+$
($y -$ )$\;^2\;\;=$
$\;^2$

The General Form is:
$x^2\;\;\;+\;\;\;$ $y^2\;\;\;+\;\;\;$
$x\;\;\;+\;\;\;$ $y\;\;\;+\;\;\;$
$=\;0$

Perimeter ≈

• Given: Standard Form of the Equation of an Ellipse
Center may or may not be at (0, 0)
Denominator is a result of squaring
To Find: other details

 $(x -$ ) $^2$ $(y -$ ) $^2$ $+$ $=\;\;\;\;\;1$

Horizontal distance from the center to the boundary =

Vertical distance from the center to the boundary =

The major axis is the

The minor axis is the

The ellipse is a ellipse

Length of the major axis =

Length of the minor axis =

Center = ( , )

Endpoints of the major axis (Vertices) =
( , )
and
( , )

Endpoints of the minor axis =
( , )
and
( , )

Foci =
( , )
and
( , )

Linear Eccentricity (distance from the center to either focus) =

Distance between the foci =

Eccentricity =

Area =

Length of the Latus Rectum =

Endpoints of the Latus Rectum passing through one focus =
( , )
and
( , )
Endpoints of the Latus Rectum passing through the other focus =
( , )
and
( , )

Distance between the two Directrixes =

The two Directrixes are

and

The Factored Form is:
($x -$ )$^2\;\;+$
($y -$ )$^2\;\;=$

The General Form is:
$x^2\;\;\;+\;\;\;$ $y^2\;\;\;+\;\;\;$
$x\;\;\;+\;\;\;$ $y\;\;\;+\;\;\;$
$=\;0$

Perimeter ≈

• Given: Standard Form of the Equation of an Ellipse, Center
Center may or may not be at (0, 0)
Denominator is squared
To Find: other details

 $(x -$ ) $^2$ $(y -$ ) $^2$ $+$ $=\;\;\;\;\;1$ $^2$ $^2$

Horizontal distance from the center to the boundary =

Vertical distance from the center to the boundary =

The major axis is the

The minor axis is the

The ellipse is a ellipse

Length of the major axis =

Length of the minor axis =

Center = ( , )

Endpoints of the major axis (Vertices) =
( , )
and
( , )

Endpoints of the minor axis =
( , )
and
( , )

Foci =
( , )
and
( , )

Linear Eccentricity (distance from the center to either focus) =

Distance between the foci =

Eccentricity =

Area =

Length of the Latus Rectum =

Endpoints of the Latus Rectum passing through one focus =
( , )
and
( , )
Endpoints of the Latus Rectum passing through the other focus =
( , )
and
( , )

Distance between the two Directrixes =

The two Directrixes are

and

The Factored Form is:
($x -$ )$\;^2\;\;+$
($y -$ )$\;^2\;\;=$
$\;^2$

The General Form is:
$x^2\;\;\;+\;\;\;$ $y^2\;\;\;+\;\;\;$
$x\;\;\;+\;\;\;$ $y\;\;\;+\;\;\;$
$=\;0$

Perimeter ≈

• Given: General Form of the Equation of an Ellipse
To Find: other details

$x^2\;\;\;+\;\;\;$ $y^2\;\;\;+\;\;\;$
$x\;\;\;+\;\;\;$ $y\;\;\;+\;\;\;$
$=\;0$

The Standard Form is:
 $(x -$ ) $^2$ $(y -$ ) $^2$ $+$ $=\;\;\;\;\;1$

Horizontal distance from the center to the boundary =

Vertical distance from the center to the boundary =

The major axis is the

The minor axis is the

The ellipse is a ellipse

Length of the major axis =

Length of the minor axis =

Center = ( , )

Endpoints of the major axis (Vertices) =
( , )
and
( , )

Endpoints of the minor axis =
( , )
and
( , )

Foci =
( , )
and
( , )

Linear Eccentricity (distance from the center to either focus) =

Distance between the foci =

Eccentricity =

Area =

Length of the Latus Rectum =

Endpoints of the Latus Rectum passing through one focus =
( , )
and
( , )
Endpoints of the Latus Rectum passing through the other focus =
( , )
and
( , )

Distance between the two Directrixes =

The two Directrixes are

and

The Factored Form is:
($x -$ )$\;^2\;\;+$
($y -$ )$\;^2\;\;=$

Perimeter ≈

• Given:
To Find:

### Calculators for Parabolas

All input values should be integers or decimals only. No fractions.
Some of the output values are in fractions and/or radicals. Pick the one you need.
Simplify further as necessary.

### Calculators for Hyperbolas

All input values should be integers or decimals only. No fractions.
Some of the output values are in fractions and/or radicals. Pick the one you need.
Simplify further as necessary.