# 6. Explain why the graph of the polar curve r = is a hyperbola. 2-4 sin 0 Where is the focal point? Where is the vertex? What are the polar equations for the asymptotes?

Q: Consider the parametric equation of the shifted ellipse 9 45 x = 4 cos 0, y = 16 sin e Evaluate the…

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Q: Describe the graph of the equation. r = 12 sin 6t i – 12 cos 6t j O Itis a circle of radius 6 in the…

A: To find: Discribe the graph of the equation

Q: 1. (a) Find a rectangular equation whose graph contains the curve C with the parametric equation…

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Q: 19T Point P is at 0 14 (1) Find polar coordinate r for P, with r > 0 and T < 0 < $. (2) Find…

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Q: r = 4 sin 0 – 2 cos e by finding a Cartesian equation of the curve. Find a polar equation for the…

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Q: 4. Find a polar equation in the form r = f(0) of the ellipse with eccentricity e = - such that one…

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Q: Write a polar equation for a conic having focus at the origin, directrix y = - 2, and eccentricity e…

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Q: Describe the graph of the equation. r = 10 cos ti + 3 sin t j – k O Itis an ellipse in the z = -1…

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Q: 18 Sketch a graph of r .Use the graph to write a Cartesian equation for the 5+ 4 sin(0) conic.

A: Sketch the graph of the conic r=185+4sin θ using a graphing calculator as shown below.

Q: Find a polar equation in the form r= f(θ) of the hyperbola with eccentricity e= 4 such that one of…

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Q: [Question 5] Write down a complete geometric description of the parametric curve x=2cos0,y=2sine,0s…

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Q: Eliminate the parameter for the following set of parametric equations x = -6 cos 4t , y = 2 sin 4t…

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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: • Question 1. Given the point R (1,4) outside the circle L = x2 + y2 -2y = 1 x² + y2 - 2y - 1 = 0…

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

A: Given :            r=7r=74+6sinθr=74+4sinθr=76+4sinθ

Q: Describe the graph of the equation. r = 2 sin 10t i + 2 cos 10t j O It is a circle of radius 10 in…

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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: Describe the graph of the equation. r = 18 cos ti + 4 sin tj -k O Itis an ellipse in the x = -1…

A: Let's find.

Q: Describe the graph of the equation. r= 2 sin 4ri + 2 cos 4tj O t is a circle of radius 2 in the…

A: Given; r=2sin4t i+ 2cos4t j

Q: 30. Show that the circle with its center at (5,) in Figure 20 has polar equation r = sin 0 + cos 0…

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

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Q: The eccentricity is given of a conic section with one focus at the origin, along with the directrix…

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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: 16.) p sin ф %3D 2

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Q: Find a Cartesian equation for the curve. r = 8 sin(0) + 8 cos(0) Identify the curve. o ellipse…

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Q: Describe the graph of the equation. r = 10 sin 17ri+ 10 cos 17t j O Itis a circle of radius 10 in…

A: Solution :-

Q: Describe the graph of the equation. r = 3 cos ti - 18 sin tj + k O An ellipse in the plane z = 1,…

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Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sinθ -3cosθ+1 at θ= π/4 5(b) Find…

A: For part 5(a): To find the slope of the tangent of the line to the given polar curve r = 2sinθ…

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: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

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

A: Given, x = atan(θ)  and y =bsec(θ) Now let us isolate tan(θ) and sec(θ) on one side of each…

Q: A curve called the folium of Descartes can be represented by the parametric equations 3t2 3t and y =…

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Q: √2 2. Consider the polar curves C₁:r = 4 + ³√² cos 0 and C₂: r = 2 - ² cos € as shown in the figure…

A: b. Consider the given polar curves, C1:r=4+322cosθ and C2:r=2-222cosθ the diagram is shown below,…

Q: Describe the graph of the equation. r = 10 sin 147 i + 10 cos 14t j O tis an ellipse in the…

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Q: For parametric equations x = a cos t and y=b sin t, describe how the values of a and b determine…

A: To determine how the parametric equation behaves :-

Q: (a) The associated parametric curve is one-half of what familar conic? Sketch the exact curve. r (t)…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

Q: 1. Sketch the graph of point P with the (2.) a. 4 2. Find the polar coordinates that correspond to…

A: We have yo plot the point P(2,3π/4) on graph

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

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Q: Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of…

A: One of the foci            =0,0    poleeccentricity                   = 4vertex nearest to pole =…

Q: 31 3t and y =: 1+1' Convert the parametric equations to parametric form, sketch the graph and 1+1'…

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Q: The graph of the curve given by the parametric equations x= sint and y=cos2t IS a

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Q: If a projectile is fired with an initial 37. Path of a Projectile speed of t, ft/s at an angle a…

A: To find the path of the projectile motion, write t in terms of x and obtain t=xv0cosα.…

Q: t y = t + 1 II

A: Consider the given parametric equation: x=1tt=1xSubstitute the value of "t" in y=tt+1,y=1x1x+1y=11+x

Q: The ellipse x, y = 1 can be drawn with parametric equations. Assume the curve is traced clockwise as…

A: topic - parametric equation

Q: Describe the graph of the equation. r = 9 cos ti + 2 sin tj - k O tis an ellipse in the z = -1…

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Q: 1. Sketch the graph of the curve represented by the parametric equations x = 4cost, y = 4sint 0sts…

A: We have to sketch the graph of the curve and find all points where the curve has a slope of 12.

Q: Many polar curves have a lot of symmetry. For example, we have examined the graph of r = sin(20) ,…

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Q: Chapter 12, Section 12.1, Question 010 Describe the graph of the equation. r = 4 sin 6t i– 4 cos 6t…

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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.