Question #104ce

1 Answer
Apr 4, 2017

Answer:

#y^2=3sqrt(x^2+y^2)+3x-x^2#

Explanation:

Use the following formulas (given by Pythagorean theorem, definition of sine, and definition of cosine, respectively):
#color(blue)(x^2+y^2=r^2)#
#color(blue)(y=rsintheta)#
#color(blue)(x=rcostheta)#

We have to manipulate the equation so that it is possible to substitute the formulas in.

(Note that the graph of #r=3+3costheta# is a cardioid, which is not a conic section, so the rectangular form of the equation will not be in any standard form.)

#r=3+3costheta#

#color(blue)(r^2)=3r+3color(blue)(rcostheta)#

#x^2+y^2=3sqrt(x^2+y^2)+3x#

#y^2=3sqrt(x^2+y^2)+3x-x^2#

Desmos