Write the standard equation for the circle.

Question

center (2, 7), r = 4

 

center (–6, –8), that passes through (0, 0)

Answer 1

Recall the standard equation for a circle:

 

(x-h)² + (y-k)² = r²,

 

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

 

For the first case, we have that (h,k)=(2,7) and r=4, so, plugging in gives us

 

(x-2)² + (y-7)² = 16.

 

For the second case, plug in (h,k)=(-6,-8) and (x,y)=(0,0) and solve for r:

 

(0+6)² + (0+8)² = r²

36 + 64 = r²

100 = r²

10 = r.

 

Now, we have (h,k)=(-6,-8) and r=10, so, the equation becomes:

 

(x+6)² + (y+8)² = 100.