Question

2. Determine the equation of a circle if the radius is 4 units and the center lies at (3, −4).

Answer 1

Answer:

the equation of a circle if the radius is 4 units and the center lies at (3, −4) is (x-3)^2 + (y+4)^2 = 16

Step-by-step explanation:

if (a , b) be center of a circle , r be radius of a circle

then the equation of the circle is (x-a)^2 + (y-b)^2 = r^2

in the given problem , to Determine the equation of a circle if the radius is 4 units and the center lies at (3, −4)

then radius of the circle is , r = 4

& center of the circle is , (a , b) = (3,-4)

then the equation of the circle is

(x-a)^2 + (y-b)^2 = r^2

⇒ (x-3)^2 + (y-(-4))^2 = 4^2

⇒ (x-3)^2 + (y+4)^2 = 16

therefore  the equation of a circle if the radius is 4 units and the center lies at (3, −4) is (x-3)^2 + (y+4)^2 = 16