6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the one that correctly shows a possible equation for C in polar coordinates and the equation of a line tangent to the pole. 27 A) C:r=1+2sin(8), With tangent to the pole 3 7T B) C :r=1+2sin(8), With tangent to the pole C) C:r=1-2 cos(6), With tangent to the pole %3D 3 27 D) C:r=1+2 cos(8), With tangent to the pole 3 ||

Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

Q: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

A: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

Q: The polar equation for the curve whose rectangular(cartesian)equation xy 2 is: (a)rcos@sine = 4 8…

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Q: Solve parts a) and b). a) Find all polar coordinate representations (r.0) where 0ses 2n of the…

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Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 2πC). (1.) Show that…

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Consider the curve C of equation (2x² – y + y³)² = a² + y? From the choices given, select the one…

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Q: 3. Rewrite the polar equation in rectangular, rewrite it either as a conic section or in the form y…

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Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

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Q: The Cartesian coordinates of a point are given. (a)     (−9, 9)   (i) Find polar coordinates  (r,…

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Q: Consider the polar curve given by the equation r(0) = 1 - sin(30). It is an example of what is…

A: Graph:

Q: Find a polar equation corresponding to the given rectangular equation. y= 15 1 sec(0) r= 15csc(0) r=…

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Q: Given polar curve r = −6 sin(θ) do the following. (a) Find the Cartesian equation for this curve.…

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Q: 3. Sketch the curve with polar equation r = cos(30), 0≤ 0 < 2π, plotting only the

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Q: Replace the polar equation given with its equivalent Cartesian form and describe the graph. a) r…

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Q: Consider the polar curve with equation r=1+2cos(θ):   (I) The slope of the tangent line to the curve…

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Q: 1. Transform the polar equation 4 cos 0 cos² 0 + 1 into its Cartesian form and identify the curve.

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Q: Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve…

A: (a) Given equation in polar coordinate is Noted that curve is symmetrical about the line ,also…