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Semi Major Axis of Ellipse given Area and Eccentricity Formula

GoSemi Major Axis of Ellipse given Linear Eccentricity and Semi Minor Axis Formula

GoSemi Major Axis of Ellipse given Area and Semi Minor Axis Formula

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Semi Major Axis of Ellipse is half of the chord passing through both the foci of the Ellipse. Check FAQs

a = \sqrt{\frac{A}{π \cdot \sqrt{1 - e^{2}}}}

a - Semi Major Axis of Ellipse?A - Area of Ellipse?e - Eccentricity of Ellipse?π - Archimedes' constant?

Semi Major Axis of Ellipse given Area and Eccentricity Example

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Here is how the Semi Major Axis of Ellipse given Area and Eccentricity equation looks like with Values.

Here is how the Semi Major Axis of Ellipse given Area and Eccentricity equation looks like with Units.

Here is how the Semi Major Axis of Ellipse given Area and Eccentricity equation looks like.

10.0398 = \sqrt{\frac{190}{3.1416 \cdot \sqrt{1 - {0.8}^{2}}}}

10.0398m = \sqrt{\frac{190m²}{3.1416 \cdot \sqrt{1 - {0.8m}^{2}}}}

10.0398 = \sqrt{\frac{190}{3.1416 \cdot \sqrt{1 - {0.8}^{2}}}}

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Semi Major Axis of Ellipse given Area and Eccentricity Solution

Follow our step by step solution on how to calculate Semi Major Axis of Ellipse given Area and Eccentricity?

FIRST Step Consider the formula

a = \sqrt{\frac{A}{π \cdot \sqrt{1 - e^{2}}}}

Next Step Substitute values of Variables

∴

a = \sqrt{\frac{190m²}{π \cdot \sqrt{1 - {0.8m}^{2}}}}

Next Step Substitute values of Constants

∴

a = \sqrt{\frac{190m²}{3.1416 \cdot \sqrt{1 - {0.8m}^{2}}}}

Next Step Prepare to Evaluate

∴

a = \sqrt{\frac{190}{3.1416 \cdot \sqrt{1 - {0.8}^{2}}}}

Next Step Evaluate

∴

a = 10.0398272208673m

LAST Step Rounding Answer

∴

a = 10.0398m

Semi Major Axis of Ellipse given Area and Eccentricity Formula Elements

Variables

Constants

Functions

Semi Major Axis of Ellipse

Semi Major Axis of Ellipse is half of the chord passing through both the foci of the Ellipse.

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Major Axis of Ellipse

Area of Ellipse

Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Ellipse

Eccentricity of Ellipse

Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.

Symbol: e

Measurement: LengthUnit: m

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Ellipse

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Semi Major Axis of Ellipse

Go Semi Major Axis of Ellipse given Linear Eccentricity and Semi Minor Axis

a = \sqrt{b^{2} + c^{2}}

Go Semi Major Axis of Ellipse given Area and Semi Minor Axis

a = \frac{A}{π \cdot b}

Go Semi Major Axis of Ellipse

a = \frac{2a}{2}

Go Semi Major Axis of Ellipse given Eccentricity and Semi Minor Axis

a = \frac{b}{\sqrt{1 - e^{2}}}

Other formulas in Major Axis of Ellipse category

Go Major Axis of Ellipse

2a = 2 \cdot a

Go Major Axis of Ellipse given Area and Minor Axis

2a = \frac{4 \cdot A}{π \cdot 2b}

How to Evaluate Semi Major Axis of Ellipse given Area and Eccentricity?

Semi Major Axis of Ellipse given Area and Eccentricity evaluator uses Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))) to evaluate the Semi Major Axis of Ellipse, The Semi Major Axis of Ellipse given Area and Eccentricity formula is defined as half of the length of the chord which passes through both foci of the Ellipse and is calculated using the area and eccentricity of the Ellipse. Semi Major Axis of Ellipse is denoted by a symbol.

How to evaluate Semi Major Axis of Ellipse given Area and Eccentricity using this online evaluator? To use this online evaluator for Semi Major Axis of Ellipse given Area and Eccentricity, enter Area of Ellipse (A) & Eccentricity of Ellipse (e) and hit the calculate button.

FAQs on Semi Major Axis of Ellipse given Area and Eccentricity

What is the formula to find Semi Major Axis of Ellipse given Area and Eccentricity?

The formula of Semi Major Axis of Ellipse given Area and Eccentricity is expressed as Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))). Here is an example- 10.03983 = sqrt(190/(pi*sqrt(1-0.8^2))).

How to calculate Semi Major Axis of Ellipse given Area and Eccentricity?

With Area of Ellipse (A) & Eccentricity of Ellipse (e) we can find Semi Major Axis of Ellipse given Area and Eccentricity using the formula - Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Semi Major Axis of Ellipse?

Here are the different ways to Calculate Semi Major Axis of Ellipse-

Semi Major Axis of Ellipse=sqrt(Semi Minor Axis of Ellipse^2+Linear Eccentricity of Ellipse^2)
Semi Major Axis of Ellipse=Area of Ellipse/(pi*Semi Minor Axis of Ellipse)
Semi Major Axis of Ellipse=Major Axis of Ellipse/2

Can the Semi Major Axis of Ellipse given Area and Eccentricity be negative?

No, the Semi Major Axis of Ellipse given Area and Eccentricity, measured in Length cannot be negative.

Which unit is used to measure Semi Major Axis of Ellipse given Area and Eccentricity?

Semi Major Axis of Ellipse given Area and Eccentricity is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Semi Major Axis of Ellipse given Area and Eccentricity can be measured.

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