Explanation Given information: The given conic equation is 10 x 2 + 6 x y + 2 y 2 − 11 = 0 . Concept used: If the x -axis and y -axis are rotated through an angle θ , then the coordinates ( x , y ) of a point P determined by the xy -plane and the coordinates ( x ' , y ' ) of the point P determined by the formula: x = x ' cos θ − y ' sin θ y = x ' sin θ + y ' cos θ Calculation Used: First, we have to convert xy -coordinates to x’y’ -coordinates. Substitute the value of cos θ = 3 10 10 and sin θ = 10 10 in the formula x = x ' cos θ − y ' sin θ , we get x = x ' ( 3 10 10 ) − y ' ( 10 10 ) = 10 10 ( 3 x ' − y ' ) Substitute the value of cos θ = 3 10 10 and sin θ = 10 10 in the formula y = x ' sin θ + y ' cos θ , we get y = x ' ( 10 10 ) + y ' ( 3 10 10 ) = 10 10 ( x ' + 3 y ' ) Substitute the value of x and y in the equation 10 x 2 + 6 x y + 2 y 2 <

2nd Edition

ISBN: 9780321825391

Author: Ratti

Publisher: PEARSON

See similar textbooks

Question

Chapter 8.5, Problem 26E

To determine

To calculate:

The equation for the given conic 10x2+6xy+2y2−11=0 in the x'y' -coordinates when the coordinate axes are rotated through an angle cosθ=31010 and sinθ=1010.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 25E

Chapter 8.5, Problem 27E

Students have asked these similar questions

8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

can you solve this question step by step please

Chapter 8 Solutions

Precalculus: A Unit Circle Approach

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

Knowledge Booster

The equation for the given conic 10 x 2 + 6 x y + 2 y 2 − 11 = 0 in the x ' y ' -coordinates when the coordinate axes are rotated through an angle cos θ = 3 10 10 and sin θ = 10 10 .

Solution Summary: The author explains the equation for the given conic, which is 10x2+6xy+2

To calculate:

The equation for the given conic 10x2+6xy+2y2−11=0 in the x'y' -coordinates when the coordinate axes are rotated through an angle cosθ=31010 and sinθ=1010.

Want to see the full answer?

Chapter 8 Solutions

The equation for the given conic 10 x 2 + 6 x y + 2 y 2 − 11 = 0 in the x ' y ' -coordinates when the coordinate axes are rotated through an angle cos θ = 3 10 10 and sin θ = 10 10 .

Solution Summary: The author explains the equation for the given conic, which is 10x2+6xy+2

To calculate: The equation for the given conic 10x2+6xy+2y2−11=0 in the x'y' -coordinates when the coordinate axes are rotated through an angle cosθ=31010 and sinθ=1010.

Want to see the full answer?

Chapter 8 Solutions

To calculate:

The equation for the given conic 10x2+6xy+2y2−11=0 in the x'y' -coordinates when the coordinate axes are rotated through an angle cosθ=31010 and sinθ=1010.