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Equation of an Ellipse

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25*y^2 + (10/sqrt2)*y*z + 4*z^2 - 50 = 0

I know when compared with the standard 2nd degree conic equation that this is an ellipse rotated 16.24 degrees.

My question is , How do I put this equation in the standard form of an ellipse equation?
ie: y^2/a^2 + z^2/b^2 = 1

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An equation is written in standard form for an ellipse. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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The idea is to remove the cross term a*yz by choosing a suitable angle theta if we rotate the coordinate system.

Please see the attached file for the complete solution.
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equation of an ellipse
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25*y^2 + (10/sqrt2)*y*z + 4*z^2 - 50 = 0 ................(*)

This is the equation I have. I know when compared with ...

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
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• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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