ASAP : What is the y-coordinate of the center of the circle for the following circle equation? x2 + y2 - 10y + 18x = 2

y = 5

Step-by-step explanation:

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 ad r is the radius

Given

x² + y² - 10y + 18x = 2 ( Rearrange collecting x and y terms together )

x² + 18x + y² - 10y = 2

Using the method of completing the square

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

x² + 2(9)x + 81 + y² + 2(- 5)y +25 = 2 + 81 + 25

(x + 9)² + (y - 5)² = 108 ← in standard form

with centre = (- 9, 5 )

The y- coordinate of the centre is therefore y = 5

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step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: