Without actually graphing, identify the type of graph that eac...

Question

Without actually graphing, identify the type of graph that each equation has.

$x^2+y^2=144$

Accepted Answer

Hello. In this video, we are going to be determining the graph that the equation represents the equation given to us is X squared plus Y squared is equal to 147. Now, one approach that we can use in order to determine the shape of the graph is to take the generic approach of the conic or in other words, we are going to be using the general form of a conic to determine which conic this equation represents. If you're not sure what the general form of a comic is, it is given to us as A X squared plus CY squared plus DX plus EY plus F is equal to zero. With this general conic. There are four conditions that follow it. The first condition is that if the coefficients of A and C are equal to each other, then this implies that the equation represents a circle. If the product of the coefficients A and C are equal to zero, then the conic or the equation represents a parabola if the coefficients of A and C are not equal to each other and the product of A and C is greater than zero. Then this conic or this equation represents an ellipse. And if the product of A and C is less than zero, the equation represents a hyperbola. So in order to use this method, we will first need to set our equation equal to zero. In order to do that, we will subtract 147 for both sides of the equation. And that will allow us to rewrite it as X squared plus Y squared minus 147 is equal to zero. Now, what we need to do is we need to identify our A NC coefficients. Our A coefficient is the coefficient in front of the X square term. There's no coefficient written but the X squared term has a coefficient of one. So that tells us that our A coefficient is equal to one. We will repeat this process for CC is the coefficient in front of the Y squared term. And just like the X squared term, the Y squared term has a coefficient of one. So our C is equal to one. Notice that the coefficients of A NC have the same value of positive one. This implies that the equation represents a circle and that means that the solution to this problem is going to be D. So I hope this video helps you in understanding on how to approach this type of problem. And I'll go ahead and see you all in the next video.

Without actually graphing, identify the type of graph that each equation has.
$x^2+y^2=144$

Key Concepts

Conic Sections

Standard Form of a Circle

Graphing Techniques

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