Question

The center of a circle is at (−2, −7) and its radius is 6.

What is the equation of the circle?


(x−2)2+(y−7)2=36

(x−2)2+(y−7)2=3

(x+2)2+(y+7)2=3

(x+2)2+(y+7)2=36



The equation of a circle is (x+4)2+(y−5)2=121.

What is the center and radius of the circle?


center: (4, −5); radius: 11

center: (−4, 5); radius: 121

center: (−4, 5); radius: 11

center: (−4, −5); radius: 121

Answer 1

1.) equation of the circle is (x+2)2 + (y+7)2 = 36
2.) center: (-4, 5) radius 11

Answer 2

1. option D is correct;
`(x+2)^2+(y+7)^2=36`

2. option C is correct; center: (-4, 5) and radius = 11 unit

Explanation:

The general equation of the circle is given by:

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

where,

(h, k) is the center of the circle and r is the radius of the circle.

1.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

⇒(h, k) = (-2, -7) and r = 6 units

Substitute these in [1] we have;

`(x-(-2))^2+(y-(-7))^2=6^2`

⇒
`(x+2)^2+(y+7)^2=36`

Therefore, the equation of circle is,
`(x+2)^2+(y+7)^2=36`

2.

As per the statement:

The equation of a circle is:

`(x+4)^2+(y-5)^2 = 121`

We can write this as:

`(x-(-4))^2+(y-5)^2 = 11^2`

On comparing with equation [1] we have;

(h, k) = (-4, 5) and r = 11 units

Therefore, the center and radius of the circle is,

center: (-4, 5) and radius = 11 unit