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

Answer:

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

Step-by-step 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:

 $(x - (-5))^2 + (y - 2)^2 = (7)^2$

 $(x +5)^2 + (y -2)^2 =49$