Convert r=8cos⁡θ+2sin⁡θ to rectangular equation

Convert

r

=

8

cos

θ

−

2

sin

θ

to Cartesian form

#x^2 + y^2 - 8 x +2 y = 0, using

r

=

√

x

2

+

y

2

≥

0

and

(

x

,

y

)

=

r

(

cos

θ

,

sin

θ

)

.

The Socratic graph of this circle,

with center at

(

4

,

−

1

)

and radius

√

17

.

is immediate.

graph{(x^2+y^2-8x+2y)((x-4)^2+(y+1)^2-0.04)=0[-1 23 -6 6] }

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

step-by-step explanation: