Question

Identify the center and the radius of a circle with equation (x-4)^2+(y+2)^2=9

Answer 1

Answer:

center:(4,-2)

Radius: 3 units

Step-by-step explanation:

The standard equation of a circle is given as $(x-h)^2+(y-k)^2=r^2$, where (h,k) is the center and r is the radius of the circle.

The given equation is $(x-4)^2+(y+2)^2=9$.

We compare to the standard equation of the circle to get;

$x-h=x-4$

$\Rightarrow -h=-4$

$\Rightarrow h=4$

and

$y-k=y+2$

$\Rightarrow -k=2$

$\Rightarrow k=-2$

Hence the center of the circle is (4,-2).

Also, we have $r^2=9$

Therefore $r=\sqrt{9}$

$r=3$ units.