Identify the conic with a focus at the origin, and then give the directrix and eccentricity. (Use the following as necessary: x and y.) 9 r = 3 + 2 cos(e)

Q: Find an equation for the conic that sa tisfies the given conditions. parabola, focus (-4, 0),…

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Q: 4. For the equation 9 r = 6+2 cos 0 (a) find the eccentricity, (b) identify the conic, (c) give an…

A: according to our guidelines we can answer only three subparts,  and rest can be reposted.

Q: Graph the line and conic section. r = 4 sec (u + pi/6)

A: General equation of a line is given as y = mx + c, where m is the slope of line and c is the…

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

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Q: Let the equation of the conic r = 2/( 1 − cos(θ))

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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: 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: а) Given a pair of parametric equations x =1-2t, y =r +4. i. Eliminate the parameter of t to obtain…

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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: Identify the conic the polar equation represents and give the position of the directrix. 1 1-sin 0…

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Q: Rotate the coordinate axes to remove the xy-term. Then name the conic section and sketch its graph.…

A: Given: x2+4xy-2y2-6=0 To Find: Rotate the coordinate axes to remove the xy-term.Then name the conic…

Q: Determine the type of conic, angle of rotation needed to eliminate the XY-term to the nearest degree…

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Q: Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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: Give the eccentricities of conic sections with one focus at the origin of the polar coordinate…

A: Solution:- Eccentricities of conic is, e=1 Directrix is  r cos u=-4 That is, x=-4 Now polar…

Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: 5) a) Find the eccentricity, b) identify the conic, c) give an equation of the directrix & d) Sketch…

A: Concept: We know that a conic section is defined as the locus of a point that moves in such a way…

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: Write the name of the conics given by polar curve r=6/(2+sin(t)) a) Determine the equation of the…

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Q: Given the following conic section, determine its shape and then sketch its graph. a? – 2ry + y² + x…

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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: Given the following conic section, determine its shape and then sketch its graph. a – 2xy + y² +x –…

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

A: Topic-polar equation

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

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

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Q: Find a polar equation of the conic in terms of r with its focus at the pole. Eccentricity e = 5/6…

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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 polar equation of a conic section, whose eccentricity e = 5 and the directrix x = 7 is 35 r= 1-5…

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Q: Identify the type, the eccentricity, the vertices, and equation of the directorix of the following…

A: Given:Identify the type, the eccentricity, the vertices, and equation of the directrix of the…

Q: Eliminate the parameter, An ellipse: x = h + a cos t, y = k + b sin t. Write the resulting equation…

A: Let's consider the given equations for the ellipse:…

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

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Q: A conic is given by 1 r = 1+2 cos 0 (a) Find the equation of the conic in rectangular coordinates.…

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

A: Please see the explanation below

Q: Find the type of conic represented by the equation of the curve given by C=21 - 6xy+29y +6x-…

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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: Use the following conic sections to answer: x? – 2x + 2y? – 8y +7 = 0 a. Graph the conic section b.…

A: Consider the given equation:…

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 the focus, orientation and external conic x?_2ny +y?+2xbys3Q 1. center of the

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

A: Given:

Q: For the equation r = directrix, and the eccentricity. 2–2 sin 6 » identify the conic with focus at…

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Q: Find the type, the eccentricity, vertices, foci, and directorices of the following conic section.…

A: The two formulas representing conics with eccentricity e are

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

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.