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17.1 equation of a circle evaluate homework and practice

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Lanuelidn

Based on the calculations, the radius of this circle with the given equation is equal to 5 units.

Given the following data:

  • [tex]x^2+y^2+8x-6y+21=0[/tex]

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where:

  • h and k represents the coordinates at the center.
  • r is the radius of a circle.

Expanding the equation, we have:

[tex]x^2+y^2-2hx-2ky+(h^2+k^2-r^2)=0\\\\r=\sqrt{h^2+k^2}[/tex]

Comparing the terms, we have:

[tex]-2hx = 8x\\\\-2h=8\\\\h=\frac{8}{-2}[/tex]

h = -4

[tex]-2ky = -6y\\\\-2k=6\\\\k=\frac{6}{-2}[/tex]

k = 3.

Now, we can determine the radius:

[tex]r=\sqrt{-4^2+3^2}\\\\r=\sqrt{16+9} \\\\r=\sqrt{25}[/tex]

r = 5 units.

Read more on circle here: https://brainly.com/question/14078280

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