The paint Pla cose,b sine) lies on the ellipre at %3D where a and b are semi- major and semi -minor axes respectively of the ellipse

Q: Find a set of parametric equations for the conic section or the line. Circle: Center:(5,3); Radius:2

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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: Write the polar equation of a conic with focus at the origin and the given data: ellipse,…

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Q: 2 ydx to compute the arca of the ellipse ()* + )= = 1. 16. Use

A: Given an ellipse with the equation We need to find the area of the ellipse using

Q: Find the eccentricity and the distance from the pole to the directrix of the conic. Then identify…

A: The standard form of the polar equation for a conic is  r=ep1±ecosθ Where e>0 is the eccentricity…

Q: Graph the line and conic section. r = 8/(1 - sin u)

A: We can convert this into rectangular form. Then,…

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

A: Given the polar equation

Q: Let a, b > 0. (a) Calculate the area inside the ellipse given by the equation 1. 62 || a²

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Q: Show that a conic with focus at the origin, eccentricity ,and directrix y=-d  has polar equation r…

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Q: Show that e² for a standard ellipse of eccentricity e. a

A: Consider the general ellipse: Horizontal:x−h2a2+y−k2b2=1a>bVertical:x−h2b2+y−k2a2=1a>b

Q: Show that the horizontal traces of the ellipsoid are ellipses of the same eccentricity (apart from…

A: To show Horizontal traces of the ellipsoid x2a2+y2b2+z2c2=1are ellipses of  same eccentricity

Q: If you are given the standard form of the polar equation of a conic, how do you determine the…

A: Consider that standard form of the polar equation of conic: Determine the location of directrix from…

Q: The major axis of the elliptical path in which the earth moves around the sun is approximately…

A: Use the properties of ellipse and formula for apogee.

Q: Find the standard form of the equation of the conic section satisfying the given conditions:…

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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: Discuss the relationship between the eccentricity e of an ellipse and the distance z between the…

A: Consider the equation of an ellipse r= Where e is the eccentricity and 0<e<1.

Q: Find the standard form of the equation of the conic section satisfying the given conditions,…

A: According to the question, we have to find the standard form of the equation of parabola whose focus…

Q: Find a polar equation for the conic Parabola with its focus at the pole and the eccentricity e = 1…

A: Focus is at pole and the eccentricity e=1 and directrix x=5. The equation of the parabola with…

Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a…

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Q: this conic is rotated counter-clockwise about the origin through an angle 37/4, rite the resulting…

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Q: Find the focus equation of the directrices, length of major axis, minor axis and focal diameters and…

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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: Identify the conic that each polar equation represents.Also,give the position of the directrix.

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Q: give the eccentricities of conic sections with one focus at the origin along with the directrix…

A: The eccentricity of a conic section is a deviation of the curve from the circularity. In simple…

Q: Identify the conic that each polar equation represents.Also,give the position of the directrix.

A: A conic section is obtained from the intersection of a plane with surface of a cone. Three types of…

Q: Name the conic that has the given properties and find its Cartesian equation. Eccentricity 1,…

A: A conic section is obtained by slicing the cones at different angles. There are three types of…

Q: Find the equation of the conic with focus at the origin, eccentricity e and the directrix y = d.

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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: The ellipse 32 = 1 can be drawn with parametric equations where x(t) is written in the form 72 x(t)…

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Q: Find the eccentricity and directrix of the conic and graph the conic and its 1-2sin 0 directrix. If…

A: Since you have asked only part B

Q: Show that a conic with focus at the origin, eccentricity e ,and directrix x = - d has polar…

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Q: Write a polar equation of a conic with the focus at the origin and the given data. parabola,…

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Q: Find parametric equations for an object moving clockwise along the ellipse 25 =1 beginning at (0,2)…

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

A: let d be positive, a directrix x = d, and focus is at the origin.

Q: Identify the conic section that appears in the drawing of a wooden pencil in the figure.

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Q: Find a polar equation for the ellipse with the following characteristics. Focus: (0, 0)…

A: To find A polar equation for the ellipse with the following characteristics. Focus: (0, 0)…

Q: Prove: If a signal (in the form of a light, sound, or other type of wave) has its source at one…

A: We need to prove that if a signal has its source at one focus of an ellipse and meets a point on the…

Q: The ellipse 82 =1 can be drawn with parametric equations where a(t) is written in the form 72 2(t) =…

A: Parametric equation of ellipse is  x = a cost  y = b Sint  In this question,  a = 8 , b = 7

Q: The vertices of an ellipse of eccentricity 0.5 lie at the points (0, +-2). Where do the foci lie?

A: The vertices of an ellipse of eccentricity is 0.5 lies on (0,+-2). Find the foci

Q: Find and sketch the polar equation for conic section with eccentricity (e = 1) and with one of the…

A: Equation of conic with eccentricity e=1 is a parabola  focus =(0,0) directrix y=-1 (0.-1) vertex…

Q: Write a polar equation of a conic with the focus at the origin and the given data. ellipse,…

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Q: Name the conic that has the given properties and find its Cartesian equation. Vertices (±4, 0) and…

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Q: Graph the ellipse $r=2 /(4-3 \cos \theta)$ and its directrix. Also graph the ellipse obtained by…

A: Given data:     The given equation of the ellipse is: r=2/(4-3cosθ).     The given equation of…