be the equation 12x2 + 12x y + 7y2 − 4x + 6y − 1 = 0. a)  Determine the nature of the conic. b) Find the angle that eliminates the mixed term.

Q: etermine which conic is the one whose general equation has only one term raised to the square, that…

A: Given:

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate,of the conic sections x2 +…

A:

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

A: The given equation is 16x2+4y2=1. The general equation of the ellipse is x2a2+y2b2=1 and b>a.…

Q: What is the relation of the conic section to the vase?

A: Let's find.

Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: Identify the type of conic, assuming a > 0: r = 1+ V7sine Ellipse. O Parabola. O Hyperbola.

A:

Q: Identify the conic represented by the equation y2 + 4x + 2y - 15 = 0 without completing the square.

A: to identify the conic represented by the equation  y2+4x+2y-15=0

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

A:

Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: Which conic section is represented by the equation 9x2 + 4y = 36- O Circle O Hyperbola O Ellipse…

A: Given equation is 9x2+4y2=36............(1)

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic section y2 -…

A: y2-4x2+16x=24 On simplification, we get…

Q: Identify the conic represented by equation 4x2 - 9y2 - 8x + 12y - 144 = 0 without completing the…

A: Given 4x2 - 9y2 - 8x + 12y - 144 = 0

Q: Identify the conic section given by the following equation. x² + y² = 78x – 84y – 3116 - Select the…

A:

Q: What conic section is described by the following equation? 4.x2 + y? + 8x + 4y = 15 O Parabola O…

A:

Q: Determine the distance between the foci of the following conic section: 16x2 + 9y- 64x 54y+1 = 0

A:

Q: Find the equation of the conic in the rotated system that eliminates the cross-product term and find…

A: Given

Q: Identify the conic represented by the equation x2 + 16y2 - 160y + 384=0 without completing the…

A: we know that equation ax2+by2+2gx+2fy+2hxy+c=0 will represent  ellipse, if h2<ab,…

Q: Determine the type of conics for each equation using the discriminant. 24. 4x2+y2 +24x-4y+36 = 0 25.…

A:

Q: Name the type of conic section defined by the following equation and give a parametrization of it:…

A: We know general equation of circle is given by  center at (a, b) of radius r is given by (x-a) ^2…

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

A:

Q: Which conic section is represented by the equation 2-8y+y + 11 = 0? O Ellipse Circle Parabola…

A: Use equation of circles that is x^2+y^2=r^2

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

A: Given 5x2+4y2=1 This equation becomes  x215+y214=1x2152+y2122=1 Comparing with the equation,…

Q: In each part, rotate the solid figure about the origin exactly onto the dashed figure. If this is…

A: We want to check whether we get the dashed figure on rotating the given figure marked in blue…

Q: Identify the conic section given by the following equation. æ? + 30x – 4y? – 168y – 1639 - Select…

A: Please refer the attached image for complete solution.

Q: Find an equation of the conic in the rotated coordinates, and find the angle of rotation. 7x2 + 8xy…

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Q: Which of the following conics has an eccentricity greater than 1?

A: The general form of the conic is given by: Ax2+Cy2+Dx+Ey+F=0 Condition for deciding what the conic…

Q: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

Q: Identify the conic sections below by completing the square on z and y to place them in standard…

A: The given equation is a) 4x2+3y2+8x-24y+40=0

Q: 4. Classify the following conics as a circle, parabola, ellipse or hyperbola and explain why. a) 9x?…

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Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5), and…

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Q: Identify the type of conic section whose equation is given and find the vertices and foci. y? – 2 =…

A:

Q: Identify the conic sections represented by the following formula a) 2x2 – 8xy + 4x = 12 b) x? + y -…

A: General form of any conic is given as- ax2+2hxy+by2+2gx+2fy+c=0—(1) We need to identify the conic…

Q: 5. Which conic section is represented by the equation 36x² + 8y = 81? %3D Hyperbola Circle Ellipse…

A:

Q: Determine the length of the latus rectum and distance between the foci of the conic section: 16x^2…

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Q: 2. Identify the conic as a hyperbola, parabola, or ellipse and find the foci: (r - 3)2 (y+1)² (b) 4…

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Q: What does the eccentricity reveals about the conic?

A: We have to define what eccentricity reveals about the conic

Q: 1) Be the equation:      4x^2 − 24x y + 11y^2 + 56x − 58y + 95 = 0. 1a) Determine the nature of…

A:

Q: Which conic section is represented by the equation 2x2 + 4x - y+9= 0?

A:

Q: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

A:

Q: Identify the conic represented by equation y2 + 4x + 2y - 15 = 0 without completing the square.

A: y2+4x+2y-15=0

Q: be the equation 12x2 + 12x y + 7y2 − 4x + 6y − 1 = 0. a)  Determine the nature of the conic. b) Find…

A: Given

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5) , and…

A: The foci of Hyperbola are:   (0, -5)  and  (0, 5). Length of transverse axis of Hyperbola is:  2a…

Q: What is the distance from the center to the foci of the ellipse given by (2-3) (y+5) 26 1? 10

A: Please refer the attached image for complete solution. THANK YOU.

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: (a) What is the eccentricity of a conic section?

A:

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate,of the conic sections x2 +…

A: Ellipse standard equation: x-h2a2+y-k2b2=1 is the ellipse standard equation with center h,k and a, b…

Q: Which conic section is represented by the equation 9x2+4y2=36

A: Simple conic section problem......