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Chapter 7: Problem 87

Will help you prepare for the material covered in the next section. Divide both sides of \(4 x^{2}-9 y^{2}=36\) by 36 and simplify. How does the simplified equation differ from that of an ellipse?

Short Answer

Expert verified
After division and simplification, the equation transforms to \(x^{2}/9 - y^{2}/4 = 1\) which represents a hyperbola, not an ellipse due to the presence of a negative sign between the terms.

Step by step solution

01

Initial Set Up

The goal is to divide both sides of the given equation \(4 x^{2}-9 y^{2}=36\) by 36, resulting in a more simple equation.
02

Divide Both Sides

Divide both sides of the original equation by 36. This yields \((4 x^{2})/36 - (9 y^{2})/36 = 36/36\).
03

Simplify

Next is to simplify the above equation. Algebraically simplify to get \(x^{2}/9 - y^{2}/4 = 1\b).
04

Comparison with Ellipse Equation

An equation of an ellipse usually comes in the form \[ (x-h)^{2}/a^{2} + (y-k)^{2}/b^{2} =1 \]. Yet, the simplified equation has a term with a negative sign, which is against the form of the ellipse. Therefore, it differs because the sign between the terms in the equation indicates that this is a hyperbola and not an ellipse.

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Most popular questions from this chapter

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