Convert the rectangular equation to polar form. Assume
a > 0.
x^2 + y^2 - 9ax=0
just crank it out
r^2 - 9arcosθ = 0
r = 9a cosθ
you know it's just a circle with center at (9a/2,0) and radius 9a/2.
To convert the given rectangular equation to polar form, we need to express the variables x and y in terms of the polar coordinates r and θ.
In polar coordinates, x and y are related to r and θ as follows:
x = r * cos(θ)
y = r * sin(θ)
Now let's substitute these expressions into the given equation:
x^2 + y^2 - 9ax = 0
(r * cos(θ))^2 + (r * sin(θ))^2 - 9a(r * cos(θ)) = 0
Expanding and simplifying this equation gives us:
r^2 * cos^2(θ) + r^2 * sin^2(θ) - 9a * r * cos(θ) = 0
r^2 * (cos^2(θ) + sin^2(θ)) - 9a * r * cos(θ) = 0
Using the trigonometric identity cos^2(θ) + sin^2(θ) = 1, the equation simplifies further:
r^2 - 9a * r * cos(θ) = 0
Now, we have the polar form of the equation:
r^2 - 9a * r * cos(θ) = 0
This is the transformation of the given rectangular equation to polar form.