Question

The center of a circle is at (−5, 2) and its radius is 7. What is the equation of the circle? (x−5)2+(y+2)2=14 (x+5)2+(y−2)2=49 (x+5)2+(y−2)2=14 (x−5)2+(y+2)2=49

Answer 1

The standard equation of a circle is in the form:

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

where; a is the x coordinate of the center, b is the y coordinate of the center, and r is the radius of the center.

In this case, a is -5, b is 2, and r is 7.

Therefore, the equation of this circle would be

(x+5)^2 + (y-2)^2 = 49

Answer 2

Second option:
`(x +5)^2 + (y -2)^2 =49`

Explanation:

The center-radius form of the circle equation is:

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

Where "r" is the radius and the center is at the point
`(h,k)`

Since the center of this circle is at the point
`(-5, 2)`, we can identify that:

`h=-5\\k=2`

We know that the radius is 7, then:

`r=7`

Now we must substitute these values into the equation
`(x - h)^2 + (y - k)^2 = r^2` to find the equation of this circle.

This is:

`(x - (-5))^2 + (y - 2)^2 = (7)^2`

`(x +5)^2 + (y -2)^2 =49`