How do you convert # x^2 + y^2 = 5# to polar form?

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Answer 1 · 2018-08-04T03:03:59

#" "#
The given equation in

Cartesian Form or Rectangular Form #color(red)(x^2+y^2=5#

can be converted to Polar Form as:

#color(blue)(r=+- sqrt(5#

#" "#
The given equation is in

Cartesian Form or Rectangular Form #color(red)(x^2+y^2=5#

We need the following formula to convert to Polar Form:

#color(blue)(r^2=x^2+y^2#

#rArr r=sqrt(x^2+y^2#

#color(blue)(x=r cos theta#

#color(blue)(y=r sin theta#

#color(blue)(tan theta = (y/x)#

#rArr theta = tan^(-1)(y/x)#

We have the Cartesian form:

#x^2+y^2=5#

Since, #color(blue)(r^2=x^2+y^2# we can write

#r^2=5#

#r = +- sqrt(5)#

This the equation in Polar Form.

Hope it helps.