Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. Bx2 - 6xy + By2 – 40 = 0 (a) Identify the resulting rotated conic. parabola hyperbola ellipse (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: 4x^2-3y^2-8x+12y+4=0

A: Given the equation of a conic, we have to identify the conic

Q: Identify the conic section that equation 16x^2-96x+288=9y^2 represents and find either: a) it’s foci…

A: We use completing square method to convert it into standard form

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…

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

Q: 4x2+y2-16y+8y+16=0 Identify the conic section by rewriting it in standard graphing form.

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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 4x2 - 9y2 - 8x + 12y - 144 = 0, without completing…

A: 4x2-9y2-8x+12y-144=0 Comparing with Ax2+By2+Cx+Dy+E=0, we get A=4, B=-9, C=-8, D=12 & E=-144

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: 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…

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

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

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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 the axes to eliminate xy term in the…

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Q: Identify the conic represented by the equation, 5x2 + 2√3xy + 3y2 - 18 = 0 without using a rotation…

A: The equation Ax2+Bxy+Cy2+Dx+Ey+F=0 a) Parabola: If B2-4AC=0 b) Ellipse: If B2-4AC<0 c) Hyperbola:…

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

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.7x2 − 6√3xy +…

A: Given that, 7x2 − 6√3xy + 13y2 − 64 = 0 Compare the given equation with ax2 + bxy + cy2 + dx + ey +…

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

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Q: Find an equation for the conic that satisfies the given condition Parabola, Vertex (0, 0), Focus (0,…

A: We have to find out parabola equation

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

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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: Identify this conic, list the necessary parts and then graph it: 2x2 +2y2 +8x=7

A: Given the equation of conic

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: 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: For Exercise, an equation of a degenerate conic section is given. Complete the square and describe…

A: Given equation is:Completing the square:Since the equation has x and y squared terms on the left and…

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: I graphed 2x2 - 3y2 + 6y + 4 = 0 by using the procedure for writing the equation of a rotated conic…

A: The given equation is  2x2 - 3y2 + 6y + 4 = 0 . Note that there is no xy terms in the above…

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.16x2 − 24xy +…

A: To Perform a rotation of axes to eliminate the xy-term, and to sketch the graph of the conic.…

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

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

Q: Find the focus and directrix of the conic parabola in standard form: (y-3)2=-4(x-4.5)

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

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Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.7x2 − 2√3xy +…

A: Given      7x2 − 2√3xy + 5y2 = 16

Q: Identify the conic represented by the equation, 5x2 - 8xy + 7y2 - 9√5x - 9 = 0 without using a…

A: Consider the given equation of conic  5x2-8xy+7y2-95x-9=0 Now, compare the given equation of conic…

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 the xy-term in the…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.