Acircle is centered at the point (5, -4) and passes through the point (-3, 2). the equation of this circle is (x + _ )2 + (y + _ )2 = _ .

By definition, the equation of a circle, centered at point (a, b) is

Where r is the radius of the circumference, and is calculated as the distance from the center to any point belonging to the circumference.

We have the center (5, -4) and the point through which the circumference passes (-3, 2), then:

Finally, the equation of the circumference is:

Step-by-step explanation:

The formula for the equation of a circle centered at the origin (0, 0) is but when the center of the circle is not the origin, then you move it back to the center mathematically.

So we have:

Finding the radius by calculating the distance from the center to the given point:

Therefore, the equation of this circle will be:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2