Convert the equation to polar form. (Use variables r and theta as needed.) y=6x^(2)

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Convert the equation to polar form. (Use variables  r and  theta as needed.)  y=6x^(2)

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Recalling Coordinate Relationships: We start by recalling the relationships between rectangular coordinates (x, y) and polar coordinates (r, θ): x = r cos θ and y = r sin θ. We will use these to convert the given rectangular equation y = 6x^2 into polar form.Substitute into Equation: Substitute x with r cos θ and y with r sin θ into the equation y = 6x^2 to get r sin θ = 6(r cos θ)^2.Simplify the Equation: Simplify the equation by squaring r cos θ to get r sin θ = 6r^2 cos^2 θ.Eliminate r Term: Divide both sides of the equation by r to eliminate the r term on the left side, being careful to avoid division by zero. This gives us sin θ = 6r cos^2 θ.Use Pythagorean Identity: Recognize that cos^2 θ can be written as (1 - sin^2 θ) using the Pythagorean identity sin^2 θ + cos^2 θ = 1. Substitute this into the equation to get sin θ = 6r(1 - sin^2 θ).Distribute 6r: Distribute the 6r on the right side to get sin θ = 6r - 6r sin^2 θ.Rearrange Equation: Rearrange the equation to isolate terms involving r on one side. This gives us 6r sin^2 θ + sin θ - 6r = 0.Correcting Mistake: Notice that we have a quadratic equation in terms of r sin θ. Let's set r sin θ = u, then our equation becomes 6u^2 + u - 6r = 0.Now, we need to solve this quadratic equation for u. However, we realize that we have made a mistake in the previous step. The term sin θ is not multiplied by r, so we cannot simply substitute r sin θ = u. We need to correct this and go back to the step before the substitution.

Convert the equation to polar form. (Use variables $r$ and $\theta$ as needed.) $\newline$ $y=6x^{2}$

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Convert the equation to polar form. (Use variables rrr and θ\thetaθ as needed.)\newliney=6x2y=6x^{2}y=6x2

Convert the equation to polar form. (Use variables $r$ and $\theta$ as needed.) $\newline$ $y=6x^{2}$