rewrite in polar form x^2+y^2-6y-8=0
Please help totally don’t et this :/
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To rewrite the equation x^2 + y^2 - 6y - 8 = 0 in polar form, we can substitute x = r cosθ and y = r sinθ, where r represents the radius and θ represents the angle.
Substituting these values into the equation, we get:
(r cosθ)^2 + (r sinθ)^2 - 6(r sinθ) - 8 = 0
Expanding and rearranging the terms, we have:
r^2 cos^2θ + r^2 sin^2θ - 6r sinθ - 8 = 0
Using the trigonometric identity cos^2θ + sin^2θ = 1, we can simplify the equation to:
r^2 - 6r sinθ - 8 = 0
This is the equation in polar form.
To rewrite the equation in polar form, we need to express it in terms of polar coordinates.
First, let's convert the rectangular coordinates (x, y) into polar coordinates (r, θ). The conversion formulas are:
x = r * cos(θ)
y = r * sin(θ)
Next, substitute these expressions into the given equation:
x^2 + y^2 - 6y - 8 = 0
(r * cos(θ))^2 + (r * sin(θ))^2 - 6(r * sin(θ)) - 8 = 0
Simplifying the equation:
r^2 * cos^2(θ) + r^2 * sin^2(θ) - 6r * sin(θ) - 8 = 0
Since cos^2(θ) + sin^2(θ) equals 1, we can simplify further:
r^2 - 6r * sin(θ) - 8 = 0
This equation is now in polar form.