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Numerade Educator

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Problem 21 Easy Difficulty

Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

$ x^2 + 4y^2 + 9z^2 = 1 $

Answer

VIl

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Video Transcript

Okay. I have X squared, Y squared and Z squared with plus signs in between equal to one. So I know that this is a ellipse wide. Mm. All right. So what you need to do is rewrite it so that The four is 1/4 in the denominator and the nine is 1 9th in the denominator. All right. So now online X. Is the one coming out and this is why. Okay. Okay. So underneath the X is one square to one is one. So I go out to one underneath the Y squared is 1/4 and the square root of 1/4 is one half. So I go to one half on the Y. When half in -1 half. And then um underneath disease 1/9. So one third and one third on the sea. Okay. So sort of like a football or hoagie Hoagie bun. Right. And it's long on the X axis and short on the Y axis.