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Express your answer as a mixed number in simplest form.

The center of the circle is  (2, - 1) and the radius is 6 units.

What are the types of equations of a circle?

The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.

The standard equation of a circle is x² + y² = r².

The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².

Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.

We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,

(- g, - f) and radius is .

Therefore, 2gx = - 4x and 2fy = 2y.

2g = - 4 and 2f = 2.

g = - 2 and f = 1.

- g = 2 and - f = - 1.

So, The center is (2, - 1).

And the radius is, .

= .

= .

= 6 units.

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Answer:

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = = 6

Answer:

The slope is and the y-intercept is .

Explanation:

This function is written in slope-intercept form, which is .  In this form, is the slope and is the y-intercept.

In this case, and , so those are the answers to this problem.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

So we have to:

Answer: