Describe the graph of each equation as a circle, a point, or none...

Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+4x+14y=-54

Accepted Answer

Identify whether the following equation describes a circle or a point. Or if it doesn't exist in the case of a circle, identify center radius for a point, identify the coordinates. Otherwise there's nothing else we need to rent. You notice here we have an equation X squared plus Y squared plus four, X minus 12, Y plus 58 equals zero. To solve this. We need the general or standard form of a circle. The standard form of a circle is given by X minus H squared plus Y minus K squared equals are quick. Let's try to transform our equation into this form. Let's group the X S first, we have X squared plus four X and then plus Y squared minus 12 Y equals a negative 58. We'll go ahead and move 58 over now. Now to get it into our standard form, we need to complete the square with both the X and the Y complain the square. This means will form a trinomial bye. Dividing the term on our X or R Y by two and squaring it. So you notice here we have a four on our X. They'll say four divided by two square. We'll go ahead and add this result which is four to both sets X squared plus four, X plus four plus the same for the Y Y squared minus 12 Y. We have negative 12 divided by two square 36. So we add 36 here. On the right side of the equation, we have negative 58 plus four and plus 36 we then get X squared plus four, X plus four, which simplifies two X plus two squared and Y squared minus 12 Y plus 36 which simplifies to Y minus six squared. Equaling the right side of your equation negative 18. Now, this is the standard form of a circle. However, our result has a negative radius. Now we can't have a negative radius because we have an A radius. This means answer c this circle of such equation does not exist. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+4x+14y=-54

Key Concepts

Standard Form of a Circle

Completing the Square

Identifying Nonexistent Solutions

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