-2.4.27 find center and radius of circle

Click For Summary
SUMMARY

The discussion centers on determining the center and radius of the circle defined by the equation $x^2+y^2+6x+8y+9=0$. The equation is rewritten and simplified through the method of completing the square, resulting in the standard form $(x+3)^2+(y+4)^2=16$, which reveals the center at C(-3,-4) and a radius R=4. While alternative methods were inquired about, completing the square is confirmed as the most efficient technique for this problem.

PREREQUISITES
  • Understanding of completing the square in algebra
  • Familiarity with the standard form of a circle's equation
  • Basic knowledge of graphing quadratic equations
  • Proficiency in manipulating polynomial expressions
NEXT STEPS
  • Research the derivation of the standard form of a circle's equation
  • Learn about alternative methods for finding the center and radius of a circle
  • Explore the use of graphing tools like Desmos for visualizing circle equations
  • Study the application of TikZ for creating mathematical graphics in LaTeX
USEFUL FOR

Students and educators in mathematics, particularly those focusing on algebra and geometry, as well as anyone interested in enhancing their skills in graphing and visualizing mathematical concepts.

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
Determine the graph of $x^2+y^2+6x+8y+9=0$
$\begin{array}{rll}
\textsf{rewrite} &(x^2+6x )+(y^2+8y)=-9\\
\textsf{complete square} &(x^2+6x+9)+(y^2+8y+16)=-9+9+16\\
\textsf{simplify equation} &(x+3)^2+(y+4)^2=16=4^2\\
\textsf{observation} &C(-3,-4), \quad R=4
\end{array}$

hopefully ok
is there another way to do this other than complete the square

if you are inclined to do so I would be interested in a tikz code would be fore this :unsure:
 
Mathematics news on Phys.org
this is ok

completing the square is probably the most efficient technique ...

Not saying there is no other method, but I'm not familiar with any.
 
Mahalo
often when post here an alternative is suggested...
:cool:
 

Similar threads

MHB How can you solve $5^{x^2+8}=125^{2x}$ for x?
  • · Replies 8 ·
Replies
8
Views
1K
MHB S5.t.5 Find domain and asymptotes.
  • · Replies 3 ·
Replies
3
Views
1K
MHB Solve $2+5\ln{x}=21$: Find $x$
  • · Replies 5 ·
Replies
5
Views
1K
MHB 5.t.11 find x for the imaginary factors
  • · Replies 2 ·
Replies
2
Views
1K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
  • · Replies 2 ·
Replies
2
Views
1K
MHB [ASK] A Circle Which Touches the X-Axis at 1 Point
  • · Replies 2 ·
Replies
2
Views
1K
MHB Circle Equation: Solving for x^2 + y^2 + Ax + By = 0 w/y=4/3x
  • · Replies 2 ·
Replies
2
Views
1K
MHB Where is the Center of Mass of a Thin Plate with Given Boundaries?
  • · Replies 4 ·
Replies
4
Views
2K
MHB What Is the Correct Equation for the Tangent of a Circle at a Given Point?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Equation and Point Check for Circle of Radius 1
  • · Replies 1 ·
Replies
1
Views
2K