Question

The eccentricity is given by the formula $e = \sqrt{1 - \frac{b^2}{a^2}}$. The ellipse is in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ a) Calculate the eccentricity of a circle b) The equation $\frac{x^2}{67912.36} + \frac{y^2}{4664} = 1$ can be used to model the orbit of Halley's Comet, which completes one full orbit of the Sun every 76 years. What is the eccentricity of the comet?

          The eccentricity is given by the formula $e = \sqrt{1 - \frac{b^2}{a^2}}$. The ellipse is in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
a) Calculate the eccentricity of a circle
b) The equation $\frac{x^2}{67912.36} + \frac{y^2}{4664} = 1$ can be used to model the orbit of Halley's Comet, which completes one full orbit of the Sun every 76 years. What is the eccentricity of the comet?

The eccentricity is given by the formula e = √(1 - (b^2)/(a^2)). The ellipse is in the form (x^2)/(a^2) + (y^2)/(b^2) = 1
a) Calculate the eccentricity of a circle
b) The equation (x^2)/(67912.36) + (y^2)/(4664) = 1 can be used to model the orbit of Halley's Comet, which completes one full orbit of the Sun every 76 years. What is the eccentricity of the comet?

Added by Robert R.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Charles Carter

06/26/2020

Step 1

Since a circle has the same length for both its major and minor axes, we can let a=b=r, where r is the radius of the circle. Plugging these values into the formula, we get e=\sqrt(1-(r^(2))/(r^(2))) = \sqrt(1-1) = \sqrt(0) = 0. Show more…

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The eccentricity is given by the formula e=sqrt(1-(b^(2))/(a^(2))). The ellipse is in the form (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 a) Calculate the eccentricity of a circle b) The equation (x^(2))/(67912.36)+(y^(2))/(4664)=1 can be used to model the orbit of Halley's Comet, which completes one full orbit of the Sun every 76 years. What is the eccentricity of the comet? b2 The eccentricity is given by the formula e. x2 form =1 a) Calculate the eccentricity of a circle x2 y2 b)The equation 67912.36 4664 -] can be used to model the orbit of Halley's Comet, which completes one full orbit of the Sun every 76 years. What is the eccentricity of the comet?