Question

Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.

Answer 1

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

$x=r*cos(t)\\y=r*sin(t)$

Replacing on the original equation, we get:

$(x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25$

Using the identity $sin^2(t)+cos^2(t)=1$ and solving for r, we get that the polar form of the equation is:

$(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)$