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.

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`