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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .