How do you convert #r= 2cos theta# to rectangular form?

Question

60133 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-19T03:58:08

Rectangular Form #color(purple)((x-1)^2 + y^2 = 1#

Given : #r = 2 cos theta#

enter image source here

( useruploads.socratic.org )

From the diagram above,
#y = r sin theta, x = r cos theta#

But given #r = 2 cos theta#

#:. r ^2 = 2 r cos theta color(white)aaa)# Multiplying both sides by #r#

#r^2 = 2 * r cos theta = 2 x#

But #x^2 + y^2 = r^2#

Hence, x^2 + y^2 = 2x#

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

#x^2 - 2x + 1 + y^2 = 1 color(white)(aaa)# Adding 1 to both sides to complete the square.

#color(purple)((x-1)^2 + y^2 = 1#