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] }

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

answer is 33

step-by-step explanation: