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

1. option D is correct;    

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

Step-by-step explanation:

The general equation of the circle is given by:

               .....[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;

⇒  

Therefore, the equation of circle is,  

2.

As per the statement:

The equation of a circle is:

We can write this as:

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

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation: