Question

Texts: For each of the given equations, find the sine and cosine of an angle through which the coordinate axes can be rotated to eliminate the cross product term from the equation. (a) 14x^2 + 16xy + 2y^2 - 10x + 26370y - 17 = 0

Name: texts for each of the given equations find the sine and cosine of an angle through which the coordinate axes can be rotated to eliminate the cross product term from the equation a 14x2 16xy 66805
Uploaded: 2022-12-13T11:29:56-08:00
Duration: 3 min 40 s
Channel: Sri K
Description: texts for each of the given equations find the sine and cosine of an angle through which the coordinate axes can be rotated to eliminate the cross product term from the equation a 14x2 16xy 66805

          Texts: For each of the given equations, find the sine and cosine of an angle through which the coordinate axes can be rotated to eliminate the cross product term from the equation. 

(a) 14x^2 + 16xy + 2y^2 - 10x + 26370y - 17 = 0

Added by Christian C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Sri K

12/13/2022

Step 1

To eliminate the cross product term, we can use a rotation matrix. Let's rewrite the equation in matrix form: \[ \begin{bmatrix} x & y \end{bmatrix} \begin{bmatrix} 14 & 8 \\ 8 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} -10 & 26370 Show more…

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Texts: For each of the given equations, find the sine and cosine of an angle through which the coordinate axes can be rotated to eliminate the cross product term from the equation. (a) 14x^2 + 16xy + 2y^2 - 10x + 26370y - 17 = 0