The letters r and theta represent polar coordinates Write th

The letters r and theta represent polar coordinates. Write the equation in rectangular coordinates (x, y). r^2 = 6 cos theta Choose the correct equation below. A. x^2 + y^2 = 6 B. (x^2 + y^2)^3/2 = 6x C. x^2 + y^2 = 6x D. (x^2 + y^2)^3/2 = 6

Solution

We have given r²=6cos(theta)

we know that x=rcos(theta) implies cos(theta)=x/r

substitute cos(theta)=x/r into given equation

r²=6*(x/r)

r^3=6x

substitute r=sqrt(x^2+y^2) into above equation

(sqrt(x^2+y^2))^3=6x

(x^2+y^2)^3/2=6x

the correct equation is B