Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 10x2 - 6xy + 2y2 – 46 = 0 (a) Identify the resulting rotated conic. O hyperbola ellipse O parabola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Express the following equation in standard form, identify the conic section, and state the locations…

A: Conic section

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Consider the following equation: y2-4x=0. 1) write the equation in shavers standard form and…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Given quadratic equation is 10x2-18xy+10y2-45=0

Q: A certain conic that has been rotated out of the standard position has the following equation in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: The given equation is . The Principal Axes Theorem states that , for a conic whose equation is ,…

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: Solve the components of the given equation of conic sections and sketch the graph: а. 9y? — 4x2 +…

A: In this question we have to solve the following question.

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b.…

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Q: Determine the type of conic section, give its equation, and clearly graph with coordinates: 9x2 +…

A: According to the given information it is required to determine the type of conic section and graph…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Given equation  9x2-10xy+9y2-46=0 The conic section with equation ax2+bxy+cy2+dx+ey+f=0 the…

Q: Q.9: Classify and find the standard equation of the conic section 4x² +9y² + 36y-16x + 16 = 0, then…

A: Given

Q: (b) The equation 7x2 - 3xy + 5y² + 4x - 16y- 121 = 0 represents a non-degenerate conic. (i)…

A: We have to find the type of conic of given equation

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: Write the equation in standard form 4y2-9x2-18x-8y-41=0

A: 4y2-9x2-18x-8y-41=04y2-8y-9x2-18x-41=04y2-2y-9x2-2x=41y-129-x--124=1y-1232-x+1222=1 The equation…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of the axes to eliminate xy term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: 7x2 - 4xy + 7y² - 25 = 0 (a) Identify the resulting rotated conic. O ellipse parabola O hyperbola…

A: This is a problem of linear algebra, linear transformation.

Q: Identify the conic represented by the equation 16x2 + 64x + 9y2 - 54y + 1=0, without completing the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Given quadratic equation: 11x2-6xy+11y2-45=0 The general form is given by: Ax2+Bxy+Cy2+Dx+Ey+F=0 a)…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: ANSWER:

Q: Identify the conic section given the general form of its equation: 26x2-5y2-61x +361y-1072=0 a.…

A: 26x2-5y2-61x+361y-1072 = 0 is the given equation.

Q: 2. Suppose that the equation Ax + Bxy + Cy² + Dx + Ey + F = 0 represents a conic section…

A: The equation Ax2+Bxy+Cy2+Dx+Ey+F=0 represents a conic. If B2-4AC>0 , The conic represents…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: If we rotate the axes through an angle θ then old co ordinate of a point p(x,y) will change to…

Q: 2. a) Identify the conic, write in standard form and graph it: 16x? + 4y² – 64x – 24y + 36 = 0. b)…

A: a) Given: 16x2+4y2-64x-24y+36=0   To find: Standard equation of conic curve and graph it.

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

A: Given, 2y2 + 4x + 8y = 0

Q: e the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Consider the given information: The given quadratic equation is, 10x2-6xy+2y2-46=0

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

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Q: Solve the components of the given equation of conic sections and sketch the graph: a. x2 + y2 – 10x…

A: Given

Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

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Q: Consider the conic (a hyperbola) of equation 7x – 6xy – 7y² + 13x + 25y – 60 = 0 whose graph is…

A: We have to find the equation of the tangent lines to the hyperbola at the given point.

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: (b) The equation 7x2 – 3xy + 5y² + 4x – 16y – 121 = 0 - represents a non-degenerate conic. (i)…

A: (i) If a conic Ax2+Bxy+Cy2+Dx+Ey+F=0 is non degenerate then the following condition holds.

Q: Find a new representation of 11x2 – 50/3xy – 39y² + 576 = 0 after being rotated through an angle of…

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Q: A. Write this equation in standard form: ? – 4y + 6x- 8y +1= 0. Show all of your work. B. Which type…

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Q: For the equation 9x + 4y - 54x-8y-59 = 0, classify the conic section, put the equation in standard…

A: Explanation: Given that,  9x2+4y2-54x-8y-59=0   Here we use the completing the square method in term…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: Identify and graph the conic whose equation is 5x2 + 4xy + 2y2 = 6

A: Solution: Consider the given equation of conic is : 5x2 + 4xy + 2y2 = 6 Comparing the given equation…