Question

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

Answer 1

Answer:

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

Step-by-step 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

$x_{0} = 6, y_{0} = -7$

$r^{2} = 16$

$r = \pm \sqrt{16}$

The radius is the positive value.

$r = 4$

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

Answer 2

Answer:

Given equation

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

centre (6,-7)  and radius 4.

Step-by-step 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

$r = \pm \sqrt{16}$

r = 4

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