Which of the following is an equation of a circle in the xy-plane with center (-1,3) that passes through the origin?

Question

Choices:

A. (x-1)² + (y+3)² = √10

B. (x-1)² + (y+3)² = 10

C. (x+1)² + (y-3)² = √10

D. (x+1)2 + (y-3)2 = 10

 

Please help. Thank you!

 

Answer 1

An equation of the circle with center (h,k) and radius r is:                      

(x-h)² + (y-k)² = r²

 

We have (x-(-1))² + (y-3)² = r²

 

Simplify to get (x+1)² + (y-3)² = r²

 

Since (0,0) is a point on the circle, (0+1)² + (0-3)² = r²

 

                                                                             so, r² = 10

 

Equation of circle:  (x+1)² + (y-3)² = 10