Answered: Write the appropriate rotation formulas…

Write the appropriate rotation formulas so that in a rotated system the equation 6x2 - 6xy + 14y2 - 45 = 0 has no x′y′-term.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 71E: Find a system of two equations in two variables, x1 and x2, that has the solution set given by the...

See similar textbooks

Related questions

Q: Find a parametric representation of the solution set of the linear equation.3x − 1/2y = 9

A: Given equation is Where x and y are unknown.

Q: Identify the equation 10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.

A: We have to identify the equation 10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.…

Q: Find the matrix A of the quadratic form associated with the equation. 7x2 + 7y2 + 7z2 + 6xy + 6xz +…

A: We will find corresponding matrix and then its eigen values to determine final equation eliminating…

Q: 16. What is the image of (2, -2) rotated 270° counterclockwise about the origin? А (-2, -2) в (-2,…

A: Solution

Q: Classify each conic section. 23) 2y + x + 8y + 11 = 0 24) x + y + 4 = 0 25) -x + 6x + y – 6 =0 26)…

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

A: Conic section

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.xy = 3

A: We need to rotate the axes by θ = π / 4 Hence, x' = x cos(θ) + y sin(θ) = (x + y)/√2 y' = - x…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

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

Q: Write an orthogonal change of coordinates converting the equation of the conic 3x2+3y +3z+2ry+2rz…

A: Given equation , 3x² + 3y² + 3z² + 2xy + 2xz+2yz = 1

Q: Find a parametric representation of the solution set of the linear equation.2x − 4y = 0

A: To find the parametric representation of the solution set, solve the given equation for the value of…

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: Find an equation of the form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

Q: 1- Sketch the following conic sections: y2 -4y+8-4x² = 0 %3D a-. .2 b- .2 y-4y-4x =8 a 3(y – 5)2 –…

A: As per our company guidelines, we are supposed to answer only the first three subparts. Kindly…

Q: Write the equation of a conic given by x2 – 9y2 + 2x- 54y-80=0 in standard form. (x+ 1)² (y+3)? 162…

A: The objective is to write the equation of conic in standard form.

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

Q: Identify the type of conic from the discriminant.Xy-2 = 0 , =45

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

Q: Find the coordinates of the reflection without using the coordinate plane. Q(-3,5) over the y-axis.

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

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, 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: 18 Identify the center of the conic section whose equation is 5x 2 + 9y 2 - 80x + 54y + 221 = 0…

A: Solution is here

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2,1,3).

A: Given,

Q: Determine the type of conic: 16. 2x2-4xy + 8y2 +7 = 0 17. 2xy-x + y-3 = 0 %3D %3D

A: The general equation of conics is given as Ax2+Bxy+Cy2+Dx+Ey+F=0, where A,B,C,D,E and F are real…

Q: Find a parametric representation of the solution set of the linear equation.−3x + 4y − 2z = 1

Q: Identify the type of conic from the discriminant.x2+2ry +y2 + V2x-V2y-2=D0, =45°

Q: Rewrite the equation in a rotated x′y′-system without an x′y′-term. Use the appropriate rotation…

A: Consider the given equationx2+xy+y2-19=0.the general form of cartesian conic equation…

Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

Q: Find the matrix A of the quadratic form associated with the equation. 3x2 + 3y2 + 3z2 + 4xy + 4xz +…

Q: 1- Sketch the following conic sections: 2-4y+8-4x2- b- y2 -4y-4x2 = 8 C- 3(y-s)2 -7(x+1)2 =1

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

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

A: Given query is to find the equations which represents conic (circle).

Q: O Reduce the equation x + 2ry +y +4 V2x - 4V2y = 0 to the standard form and hence %3D identify the…

A: The given equation is x2+2xy+y2+42x-42y=0

Q: For the equation, 9x² +8/3xy+y²-8=0, complete the following questions. a. Rewrite the equation in a…

A: The general form of a conic equation is Ax2+Bxy+Cy2+Dx+Ey+F=0, where A, B, C are not equal to 0.

Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

Q: Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term.…

A: It is given that

Q: Find the matrix A of the quadratic form associated with the equation. 6x² + 6y2 + 6z? + 8xy + 8xz +…

A: Given 6x2+6y2+6z2+8xy+8xz+8yz-1=0

Q: find the key values for a conic a. y^2 - 8x - 4y + 4 = 0 b. 6x^2 - 4y^2 -12x-8y-22=0 c. x^2…

A: a y2-8x-4y+4=0y2-4y+4-8x=0y-22=8xwhere y=y-2 , a=2which is the general form of a parabolavertex…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

Q: Identify the equation without applying a rotation of axes. 2 10x² -8xy + y² +9x+3y-6=0

A: Given, 10x2-8xy+y2+9x+3y-6=0

Q: Determine the center of the conic of equation: 16x² + 128r + 49y² + 588y = -1236. A) (4,6) В) (-4,…

A: Brief explanation of the answer is below.

Q: Graph the image of square JKLM aftera rotation 90° counterclockwise around the origin. 6. 2. 10 -2…

A: When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes…

Q: For numbers 1 and 2: Choose the graph that corresponds to the given equation of the conic. 1. (x –…

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

Question

Write the appropriate rotation formulas so that in a rotated system the equation 6x² - 6xy + 14y² - 45 = 0 has no x′y′-term.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Rotations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.
Write the appropriate rotation formulas so that in a rotated system the equation has no x′y′-term. 3xy - 4y2 + 18 = 0
For linear algebra, how would a rotated conic be calculated using u and v as variables with an angle to the nearest tenth decimal?
When the axes are rotated through an angle 4π, find the transformed equation of3x2+ 10xy + 3y2= 9.
when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9
Given 7x^2 - 6sqrt(3)xy - 13y^2 - 16 = 0 A new equation after rotation using x = x'cos(theta) - y'sin(theta) and y = x'sin(theta) + y'cos(theta) becomes (x')^2/4 - (y')^2 = 1 Find the vertices of the conic in the xy-plane
Rewrite the equation in a rotated x′y′-system without an x′y′-term. Use the appropriate rotation formulas. For the equation, x^2+xy+y^2−19=0, answer the following question.
Find a parametric representation of the solution set of the linear equation.−3x + 4y − 2z = 1
Perform a rotation of axes to eliminate the xy-term in 5x2 − 6xy + 5y2 + 14√2x − 2√2y + 18 = 0 and sketch the graph of the resulting equation in the x′y′-plane.
Determine the coordinate of a 3D point (100.0, 29.0, -79.5) after rotating 60° across Y-axis, given that the center of rotation is (40.0, -1.0, -0.5).