Problem

Identify the graph of each equation as a parabola…

Problem 16 Easy Difficulty

Identify the graph of each equation as a parabola, circle, ellipse, or hyperbola, and then sketch the graph. See Example 3.
$$
9 x^{2}=144+16 y^{2}
$$

Answer

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Algebra

Beginning and Intermediate Algebra

Chapter 13

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Section 3

The Hyperbola and Functions Defined by Radicals

Discussion

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Video Transcript

this problem, we have nine X squared is equal to 1 44 plus 16 y Square. Now it's hard to see exactly what kind of Connick section this is going to be. So the first thing I'm going to do is I am going to subtract 16 y from both sides. Why squared from both sides? At this point, we can see that it's going to be a hyperbole because one of the terms is positive and one of them is negative. But let's keep going to make it into standard form. So we know that when I divide when I have 9/1 44 I'm going to have X squared over 16 minus y squared over nine is equal to one. This is by dividing everything by 1 44 Now it's much easier to see that this is going to be a hyperba. We know that the center of the hyperbole will be at 00 because nothing is being added or subtracted in the numerator. We know that it's going to open left and right because my ex term is positive. We're gonna open for the Vergis ease will be four units to the right and four units of the left of the center in order to figure out how wide it's going to be. I'm going to create the rectangle by going three units up in three units down from my center, and I know that because squared of nine is three, the acid totes will travel from the center through the vergis ease of the rectangle, and the hyperbole will pass through the vergis ease and snuggle up to the Assam toads, and this is what I probably would look like.

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