Question

Select the graph that represent the equation (x-6)^2+(y+7)^2=16

Answer 1

Given equation

(x-6)^2+(y+7)^2=16

centre (6,-7) and radius 4.

Explanation:

The equation of a circle is (x - a)² + (y - b)² = r²

the radius is r

the centre is (a, b)

Given equation

(x-6)^2+(y+7)^2=16

so ,

a = 6

b = - 7

r² = 16

`r = \pm √(16)`

r = 4

Therefore, the circle with centre (6,-7) and radius 4.

Answer 2

This is a circle with centre (6,-7) and radius 4.

Explanation:

The equation of a circle has the following format:

`(x - x_(0))^(2) + (y - y_(0))^(2) = r^(2)`

In which r is the radius(half the diameter) and the centre is the point
`(x_(0), y_(0))`

In this question:

`(x-6)^(2) + (y+7)^(2) = 16`

So

`x_(0) = 6, y_(0) = -7`

`r^(2) = 16`

`r = \pm √(16)`

The radius is the positive value.

`r = 4`

So this is a circle with centre (6,-7) and radius 4.