Question

17.1 equation of a circle evaluate homework and practice

Answer 1

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

Given the following data:

• $x^2+y^2+8x-6y+21=0$

The equation of a circle.

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

$(x-h)^2+(y-k)^2=r^2$

Where:

• h and k represents the coordinates at the center.

• r is the radius of a circle.

Expanding the equation, we have:

$x^2+y^2-2hx-2ky+(h^2+k^2-r^2)=0\\\\r=\sqrt{h^2+k^2}$

Comparing the terms, we have:

$-2hx = 8x\\\\-2h=8\\\\h=\frac{8}{-2}$

h = -4

$-2ky = -6y\\\\-2k=6\\\\k=\frac{6}{-2}$

k = 3.

Now, we can determine the radius:

$r=\sqrt{-4^2+3^2}\\\\r=\sqrt{16+9} \\\\r=\sqrt{25}$

r = 5 units.

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