Question

A circle has its center at (−2, 5) and a radius of 4 units. What is the equation of the circle? (x + 2)2 + (y − 5)2 = 16 (x + 2)2 + (y + 5)2 = 16 (x + 2)2 + (y − 5)2 = 4 (x − 2)2 + (y + 5)2 = 4

A circle has its center at (−2, 5) and a radius of 4 units. What is the equation of the circle?

(x + 2)2 + (y − 5)2 = 16
(x + 2)2 + (y + 5)2 = 16
(x + 2)2 + (y − 5)2 = 4
(x − 2)2 + (y + 5)2 = 4

Answer 1

See a solution process below:

Explanation:

The formula for the equation for a circle is:

`(x - color(red)(a))^2 + (y - color(red)(b))^2 = color(blue)(r)^2`

Where `(color(red)(a), color(red)(b))` is the center of the circle and `color(blue)(r)` is the radius of the circle.

Substituting the values from the problem gives:

`(x - color(red)(-2))^2 + (y - color(red)(5))^2 = color(blue)(4)^2`

`(x + color(red)(2))^2 + (y - color(red)(5))^2 = color(blue)(16)`

Answer 2

`(x+2)^2+(y-5)^2=16`

Explanation:

`"the equation of a line in standard form is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`

`"where "(a,b)" are the coordinates of the circle and r"`
`"is the radius"`

`"here "(a,b)=(-2,5)" and "r=4`

`"substitute these values into the equation"`

`(x-(-2))^2+(y-5)^2=4^2`

`(x+2)^2+(y-5)^2=16larrcolor(red)"equation of circle"`