Aline has equation y = k, where k is a constant. for which values of k does the line not intersect the circle with equation

i tried substituting k into y but i don't think that's right because i don't know what to do after that.

What you need to do is write the equation of the circle in standard form,

so that it's easy to identify the two central traits of the circle, its center and its radius .

By completing the square, we have

and from this we can tell the circle is centered at with radius 2.

The line is horizontal and will intersect the circle whenever , or . So the line will not intersect the circle if or .

yeah and the opposite of cheating is studying ( you should try it some time)

step-by-step explanation:

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 .