Answer:
Step-by-step explanation:
hello :
x² + 4x + y² − 6y = −4
(x² + 4x+4)-4 + (y² − 6y+9) -9 = −4
(x+2)²+(y-3)² = 3²
The center is located at (−2, 3), and the radius is 3
To solve this question:
Doing this, we have that: The center is located at (−2, 3), and the radius is 3.
Equation of a circle:
The equation of a circle of center [tex](x_0,y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
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The following equation is given:
[tex]x^2 + 4x + y^2 - 6y = -4[/tex]
To complete the squares, we divide each first order term(4 and -6) by two, having two new terms(2 and -3). With this, we write as the square of (x+2) and (y-3). To compensate, we have to find the square of 2 and -3 on the other side of the equality.
Thus:
[tex](x + 2)^2 + (y - 3)^2 = -4 + 2^2 + 3^2[/tex]
[tex](x + 2)^2 + (y - 3)^2 = 9[/tex]
Comparing with the standard equation, we have that:
[tex]-x_0 = 2 \rightarrow x_0 = -2[/tex]
[tex]-y_0 = -3 \rightarrow y_0 = 3[/tex]
[tex]r^2 = 9 \rightarrow r = 3[/tex]
Meaning that:
The center is located at (−2, 3), and the radius is 3.
A similar question is given at https://brainly.com/question/16505663
