Determine the shape of each polar curve. 9r = 7 parabola 7 circle 9 r = 4 + 6 sin(0) ellipse hyperbola a r = 4 + 4 sin(0) 7 6 + 4 sin(0)

Q: identify the type of conic, the eccentricity, and the equation of the directrix. r = 8/1 + 4 cos θ

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Q: Eliminate the parameter 0 in the following parametric equations. (This curve is called a hyperbola.)…

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Q: 4. Write down the name of the conic given by the polar curve r = 15 / (3 + 2 sine). Determine the…

A: We have to draw graph of given curve.

Q: Find a polar equation that has the same graph as the parabola x² = 8(2 – y) %3D

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Q: Find a polar equation in the form r= f(θ) of the ellipse with eccentricity e= 6/7 such that one of…

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Q: Graph the line and conic section. r = 1/(1 + 2 sin u)

A: Use the formula: x=rcos (u), y=rsin (u), x2+y2=r2   r (1 + 2 sin(u)) = 1r + 2r sin(u) = 1   Thus…

Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: Let D be an ellipse rotated counterclockwise by radians, as pictured below. Before rotation, the…

A: Given that                                                   ∫∫D(-6+4y)dA we have to convert it into…

Q: 9. Find other polar coordinates (r,) of the point in polar form given by (3,) for which r <0 and -2π…

A: answer is in next step . please give a like!!

Q: Q2: Discuss the symmetry and plot the locus of polar equation r-3+2sine.

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Q: Write a polar equation in rand of an ellipse with the focus at the origin, with the 8 eccentricity…

A: A polar equation  of the form r=ed1±e cosθ, r=ed1±e sin θ represents a conic with eccentricity e…

Q: Find the polar equation for a parabola with its focus at the origin and whose directrix is y = -a…

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Q: How many times do the graphs of the polar curves r=3 and θ=π/6 intersect?

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Q: Identify the conic section and graph the polar equation: r = 2/(1 - cos θ)

A: The given polar equation is r=21-cosθ Here, the given equation can be ellipse, parabola and…

Q: Q3 Write down the polar form of the equation 2 arctan(y/a)

A: convert the given equation into polar form x2+y2=e-2arctanyx

Q: Write the name of the conics giver by poloar curve r=6/(2+sin(t)) a) Determine the vertices in the…

A: We need to write the name of the conics given by the polar curve r=6/(2+sin(t)). Also, we need to…

Q: Find an approximate polar equation for the ellipticalorbit of the earth around the sun (at one…

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Q: Q1) A) Replace the polar equation r? sin 20 = 2 by equivalent Cartesian equation. B; C) Find the…

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Q: 4. Find the distance from the pole to the vertices, and then find the equation of the ellipse in…

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Q: Identify the conic that the following polar equation represents. 5 r = 10 + 5 sin 0 Select the…

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Q: Identify the conic that the following polar equation represents. 8 r = 2+2 sin 0 Select the correct…

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Q: 5. Consider the point with rectangular coordinates (1, – V3 ). sState the coordinates of the point…

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Q: Q4\ find a polar equation for the circle x² + (y - 3)² = 9

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Q: 3 Identify the conic represented by the polar equation r 1 Find the rectangular equation. 2 cos 0

A: Given equation, r=31-2cosθ                              ....(1)

Q: Which of the following two sets of parametric functions both represent the same ellipse. Explain the…

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

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Q: c) Write the polar equation for a conic section with eccentricity 3, a focus at the pole, and a…

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Q: Given a pair of parametric equations x = 2 cos(t) – 4 and y = 3+ 3 sin(t). i. Eliminate the…

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Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: identify the type of conic, the eccentricity, and the equation of the directrix.  r = 8/4 + cos θ

A: Given: r = 84 + cos θ To identify: The type of conic, the eccentricity, and the equation of the…

Q: 11. Write a polar equation of a conic with the focus at the origin given the following:…

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Q: Mark the alternative that corresponds to the radius R and the center C (in polar coordinates (r,θ))…

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Q: Find the polar equation of a hyperbola with eccentricity 2, and directrix y = 5. Select the correct…

A: We have to find the polar equation of the hyperbola with eccentricity 2 and directrix y=5.

Q: Consider the polar equation of a conic. Determine the eccentricity. -5 r = 1 + cos(0) e =

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Q: Q1) Find the polar equation of the circle whose center has polar coordinates (a, 0,) and radius a.…

A: Given a polar point (a, theta 0) and radius a.

Q: The polar equation r=2, the Cartesian equation x+y = 4, and the parametric equations x=2sin(3t) ,…

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Q: 2 Q3: Discuss the symmetry and plot the locus of polar equation r 1-cose

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Q: For the given polar curve, identify the conic, find the equation of the directrix, and sketch it: r…

A: Given curve is r=53+8sinθ. To find: 1) Identify the conic.              2) Equation of the…

Q: (b) Sketch the graph of the following polar curves 0 = n/4, for all r. Find it's equivalent forms in…

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Q: Give the equation in polar coordinates of a conic section with a focus at the origin, eccentricity…

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Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

A: We know eccentricity is the Ratio of distance between variable point to directrix to distance…

Q: Consider the following. 10 7 +7 cos(0) (a) Find the eccentricity. Identify the conic. C parabola C…

A: Given:

Q: Which of these is the polar equation of a ellipse with eccentricity , and directrix æ = 5? Select…

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Q: Eliminate the parameter to relate the variables directly in the parametric set of equations and…

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Q: Identify the conic with a focus at the origin, and then give the directrix and eccentricity. (Use…

A: r=93+2cosθ  Rearranging this, we get  r=931+23cosθ    r=31+23cosθ

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.