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Chapter 10: Q54. (page 677)

Show thatA+C=A'+C', and thus show that A+Cis invariant; that is, its value does not change under a rotation of axes.

Short Answer

Expert verified

Thus,A+C=A'+C'is invariant.

Step by step solution

01

Step 1. Given Information

Ax2+Bxy+Cy2+Dx+Ey+F=0

02

Step 2. Explanation to invariant

Consider the equation x2+4xy+4y2+55y+5=0

Here A=1,C=4gives A+C=1+4=5

The rotated equation is 0x'2+5y'2-2.35x'+4.45y'+5=0

Here A'=0,C'=5gives A'+C'=5

BothA+CandA'+C'are equal.

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