Write the Rectangular Form of the Polar Equation: r=12
we know
r^2 = x^2 + y^2
r = √(x^2 + y^2)
√(x^2 + y^2) = 12
x^2 + y^2 = 144 ---> a circle with radius 12, which is what r = 12 says.
To convert the polar equation r = 12 to rectangular form (in terms of x and y), we need to use the relationships between the polar coordinates (r, θ) and the rectangular coordinates (x, y).
In polar coordinates, r represents the distance from the origin to a point (x, y), and θ represents the angle between the positive x-axis and the line connecting the origin and the point.
To convert a polar equation to rectangular form, we use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In the given equation r = 12, we can substitute r = 12 into the formulas to find the rectangular form:
x = 12 * cos(θ)
y = 12 * sin(θ)
Therefore, the rectangular form of the polar equation r = 12 is x = 12 * cos(θ) and y = 12 * sin(θ).