Use the steps below and completing the square to show the polar equation that follows is a circle with center (1,0) and radiusr= 1.

Question

.Polar Equation:r= 2 cosθ(

i) Multiple both sides byr:r2= 2rcosθ

(ii) Express the equation in rectangular coordinates:x2+y2= 2x

(iii) Write the equation so all variables are on the left-hand-side:x2−2x+y2= 0(iv) Show the steps you need to use in completing the square towrite the equation of thiscircle in a form similar to (x−h)2+ (y−k)2=r2.

Answer 1

starting at iii...

x^2-2x+y^2=0

x^2-2x +y^2=0

take half of -2 and square it

(-1)^2=1

add 1 to both sides of the equation

x^2-2x+1+y^2=1

(x-1)^2+(y-0)^2=1^2

the center is (h,k) and the radius is r

center=(1,0) and radius=1