Question

2. Circle C, has center (0,0) and radius 2.

Answer 1

Answer:

2. x ²  +  y ² =  4

3. x² + y² = 23

Step-by-step explanation:

The equation of a circle with center  

( a , b )  and radius  r  is:

( x − a )²   +  ( y − b ) ² =  r ²

Explanation:

Here,

 a = 0 ,  b = 0 ,  r = 2  

The equation is:

( x -0 ) ² +  ( y -0 ) ² =  ( 2  ) ²

that is:  x ²  +  y ² =  4  

Thus:

x ²  +  y ² =  4

3. Each point on a circle has the same distance from the center. This distance is the radius  r  of the circle.

 Here, ( -3 , 4 )  is a point on the circle, meaning that the radius of the circle is the distance between  ( 0 , 0 ) , the center, and  ( -3 , 4 ) .

thus  a circle centered on the origin will have an equation of:

x² + y² =r²

And,  ( -3 , 4 )  lies on the circle, we have:

(-3)² + (4)² = r²

9 + 14 = 23

substituting;

x² + y² = 23