Question

Which equation represents a circle with center (5,-1) and a radius of 16 units?

A (x-5)2 + (y + 1)2 = 16
B. (x-5)² + (y+ 1)² = 256
C. (x + 5)² + (y-1)² = 16
D. (x+ 5)² + (y- 1)² = 256

Answer 1

Answer: The correct option is B.

Step-by-step explanation:

The equation of any circle with a given radius $r$ and coordinates of centre ($\alpha$,$\beta$) is given by:

$(x-\alpha )^{2} +(x-\beta )^{2} =r^{2}$

Here $r=16$ ;

$(\alpha ,\beta )$=$(5,-1)$

Plugging in the values in the given equation,

We get:

$(x-5)^{2} +(x+1 )^{2} =16^{2}=256$