Find the area of an ellipse, using the cartesian equation; check by using the equation x=a cosΦ, y=b sinΦ Pls include figure

Q: Find the eccentricity, identify the conic, and equation of the directrix. 1 r = 2 + sin 0

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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: a) Reproduce the algebra required to convert this Cartesian equation to the polar form r = sin(20).…

A: Given the algebraic equation, (x2+y2)3=4x2y2 ⋯⋯(1) (a) Take x2+y2=r2, x=rcosθ, and y=rsinθ Then…

Q: Given the polar equation of the conic with focus at the origin, identify the eccentricity and…

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Q: A 10-ft ladder slides down a wall as its bottom B is pulled away from the wall (Figure below). Using…

A: A 10-ft ladder slides down a wall as its bottom B is pulled away from the wall. It forms angle θ as…

Q: find the eccentricity, identify the conic, give an equation of the directrix and sketch the graph of…

A: Solution is given below:

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

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Q: 1. Convert the rectangular equation r2 + y? – 2ax = 0 to polar form and sket ch its grap %3D

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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: Suppose a churro is 10 inches long and has a cross-section described by the parametric equation c(t)…

A: Since cross sectional area is same throughout the length so volume is the product of length and…

Q: Identify the conic section that the polar equation represents. Describe the location of a directrix…

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Q: (a)i- Show that the following equation represents a sphere, and find its center and radius.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: . (a) Find the eccentricity and the distance from the pole to the directrix and sketch the plot in…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: A horizontal bridge is in the shape of a parabolic arch.Given the information shown in the figure,…

A: A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure…

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: Find the area of the inner loop of the limacon with polar equation r = 9 cos e – 4 01 = cos- ()…

A: The area of the inner loop of the limacon is given by: A=12∫-θ1θ1r2dθ We are given that…

Q: Find the directrix of the parabola r = 25/(10 + 10 cos θ)

A: The parabola r=2510+10cosθ, we have to find the directrix of this given parabola.

Q: A) Use polar coordinate system to sketch and find the area in side r = 8 cos0 out side x? + y? = 16.

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Q: Lithotripsy is a noninvasive medical procedure that is used to break u kidney stones in the body. A…

A: Here we have a major axis of ellipse 2a= 44.6 cm and minor axis of ellipse = 2b= 29 cm

Q: C 5 D B

A: We are asked rotate the trapezoid coordinate 180o  counter clock wise about the origin.

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

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Q: c) Find the area of the sector formed by the 2 radii (OA & OB ) and AB.

A: for the sector OAB, the area is given by  A=θ360·πr2 here we have θ=30 here diameter is 12 so the…

Q: Find a Cartesian equation for the curve.

A: By using convertion formula for converting polar coordinates in to Cartesian coordinates. We can…

Q: identify the type of conic, the eccentricity, and the equation of the directrix.  r = 12/4 + 3 cos θ

A: To find: The type of conic, the eccentricity, and the equation of the directrix. Given information:…

Q: r = 2– sin(0)"

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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: Find the area of the region in the first quadrant enclosed by one petal of the three petal rose. The…

A: Here we have to find the area of the first quadrant enclosed by one petal of the three petal rose.…

Q: A sphere has center in the first octant and is tangent to each of the three coordinate planes. The…

A: If the radius is r, then centre is (r, r, r) Given that distance between centre and origin is 3-3…

Q: identify the type of conic, the eccentricity, and the equation of the directrix. r = 8/4 + 3 cos θ

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Q: Find the constants a,b,c for the conic r = 120 5+ sin 0 Sketch the conic.

A: As per the question we are given the polar form of a conic, and from that we have to find the…

Q: The diagram shows an initial arm of length 1 unit being rotated counterclockwise about the origin to…

A: The given diagram is: To find:  ∠AOB

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: Find the area enclosed by r= 5 + 4sinθ in the Polar coordinate system, but only the part that is in…

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Q: Rewrite polar equation for hyperbola as a 48 Cartesian equation r 5 – 7 sin(0) Preview

A: Given polar equation

Q: Draw and Isometric view of a hexagonal prism of side 30 mm and height 50 mm

A: An isometric view represents the overall appearance of an object and can be used to understand the…

Q: A satelliet dish, like the one shown in the fig., is in the shape of a parabolic surface. Signals…

A: It represents an upward parabola with vertex at origin. Therefore equation of the parabola is,…

Q: A. Use polar coordinates to describe the region shown. 1.

A: From the Shaped region, clearly this is semicircle lies in upper half plane of radius 8 and centered…

Q: A satelliet dish, like the one shown in the fig., is in the shape of a parabolic surface. Signals…

A: We draw the image as, The base of the dish  is the vertex of parabola, the receiver would be at the…

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

A: Given: The function is given as ? = ?/?+?????

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

A: Given polar curve r=53+8sinθ Comparing the above form to the general form: r=ed1+esinθ Here, e is…

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

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Q: Identify the conic and write its equation in rectangular coordinates: r 2 - 2 cos 0

A: r=12-2cosθ⇒r=121-cosθ⇒r=121-cosθ Comparing with r=ep1-ecosθ, we get e=1&ep=12⇒1p=12⇒p=12 Since…

Q: Find parametric equations for the segment joining the given points. (1, 3) and (3, 6) 0 sts1 c(t)…

A: Let p and q be the points (1,3) and (3,6) The parametric equation of the segment joining p and q is…

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: His a point in the Catesia Plane Delteiraine 11) OB 2) Cos B 113) CosecB 1 tan B

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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

Q: A golf ball is struck across a flat fairway at an angle of 60° with an initial speed of 135ft/s.…

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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.