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Determine whether the given equations is a circle, a point, or a contradiction (no real graph).$$(x+4)^{2}+(y+3)^{2}+9=0$$

Contradiction

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

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In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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for this problem, we're going to examine the equation. X plus four squared Plus why plus three squared plus nine equals zero. And we want to determine what kind of a graph this is. Is it a circle? Is it a point or is it a contradiction where no riel graph, um, exists that goes along with this equation? Well, how do you know which one of those? We have to see? That we're going to need to look at the standard form for a circle that is X minus H squared. Plus why minus k squared equals R squared. And this r squared is going to tell us what this graph looks like. If R squared is any positive number, then I have a circle where the radius of our so far square to 16 My radius is four. If it's 36 my radius is six, and so on. If r squared equals zero, I have a point. You know, I I exist at at the center, but I don't go anywhere. There's no radius so arse critical. Zero gives me a point, and if I end up with an R squared, that's less than zero. That's a contradiction. And there are no riel number. Radius is when I square them, that will give me a negative number. So I'm gonna put this equation that we've been given into standard form. And by examining r squared, I can see what kind of a graph I have. So for this problem, I have X plus four squared plus why, plus three squared equals negative nine. Well, r squared is less than zero. So that's our third case. Are contradiction. There is no riel graph that goes along with this equation tradition.

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