Question #b6651

2 Answers
Apr 23, 2017

The equation is:

(x-3)^2+(y-2)^2=(sqrt117)^2

Explanation:

The standard Cartesian form for the equation of a circle is:

(x-h)^2+(y-k)^2=r^2" [1]"

where (x,y) is any point of the circle, (h,k) is the center point, and r is the radius.

Substitute the center (3,2) into equation [1]:

(x-3)^2+(y-2)^2=r^2" [2]"

Use equation [2] and the point (-6,-4), to find the value of r:

(-6-3)^2+(-4-2)^2=r^2

(-9)^2+(-6)^2=r^2

81+36=r^2

r^2 = 117

r = sqrt(117)

The equation is:

(x-3)^2+(y-2)^2=(sqrt117)^2" [3]"

Apr 23, 2017

Use distance formula to find the radius.
r = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

r = sqrt((-6 - 3)^2 + (-4 - 2)^2)

r = sqrt((-9)^2 + (-6)^2)

r = sqrt(81 + 36)

r = sqrt(117)

Now plug into equation of a circle

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

(x-3)^2 + (y-2)^2 =sqrt(117)^2

(x-3)^2 + (y-2)^2 =117