Question

Which is the equation of this circle in standard form

Answer 1

(x − 5.5)2 + (y − 4)2 = 12.25

Step-by-step explanation: Just took the test and got it right

#Plato4Life#EdmentumFam

Answer 2

The equation of a circle in standard form:

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

(h, k) - center

r - radius

The center is a midpoint of MN. The formula of a midpoint:

`\left((x_1+x_2)/(2);\ (y_1+y_2)/(2)\right)`

We have M(2, 4) and N(9, 4). Substitute:

`x=(2+9)/(2)=(11)/(2)=5.5\\\\y=(4+4)/(2)=(8)/(2)=4`

Therefore we have the center (5.5, 4) → h = 5.5 and k = 4.

The radius of a distance between the center and M.

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the points (5.5, 4) and (2, 4) Substitute:

`d=√((4-4)^2+(2-5.5)^2)=√(0^2+(-3.5)^2)=√(3.5^2)=3.5`

Substitute to the equation of a circle:

`(x-5.5)^2+(y-4)^2=3.5^2\\\\\boxed{(x-5.5)^2+(y-4)^2=12.25}\to\boxed{C.}`