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Chapter 13: Problem 43

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?

Short Answer

Expert verified
No, the given equation does not represent a circle. The graph of this equation does not represent any real coordinate points.

Step by step solution

01

Identify the form of the equation

Compare the given equation \((x-3)^{2}+(y-5)^{2}=-25\) with the standard equation of the circle \((x-h)^{2}+(y-k)^{2}=r^{2}\). Here, \(h=3\), \(k=5\) and \(r^{2}=-25\).
02

Analyze the value of the radius square

The radius square value is negative, Meaning that \(r\) would be an imaginary number since the square root of a negative number is imaginary.
03

Determine the type of set

As the radius cannot be an imaginary number for a circle, the given equation doesn't represent any real coordinate points. Hence, The graph of this equation doesn't represent a physical set or a circle.

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