Question

Find the center and radius of the circle represented by the equation below. 100pts

Answer 1

Center = (-5, -2)

Radius = 18

Explanation:

The equation of a circle in standard form is:

`\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}`

If we compare the given equation of (x + 5)² + (y + 2)² = 324 to the standard form, we get:

• h = -5
• y = -2
• r² = 324

Therefore, the center of the circle is (-5, -2).

To find the radius, square root 324:

`r^2=324 \implies r=√(324)=18`

Therefore, the radius of the circle is 18.

Answer 2

centre = (- 5, - 2 ) , radius r = 18

Explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

(x + 5)² + (y + 2)² = 324 ← is in standard form , that is

(x - (- 5))² + (y - (- 2))² = 18²

with centre = (- 5, - 2 ) and r = 18