Consider the following pairs: I. x1^2+2x1x2+x2^2; y1^2+2y1y2+y2^2 II. x1^2-2x1x2-x2^2; 2y1^2+y1y2-y2^2 III. x1^2+2x1x2-2x2^2; 2y1^2+y1y2+2y2^2 IV. x1^2+x1x2-x2^2; y1^2+y1y2-y2^2 How many of the above are non-orthogonal pairs?

Q11Section I (Objective (Q1–Q80))11 of 79

Algebra — counting non-orthogonal line-pair quadratics

Consider the following pairs:

$\text{I. } x_1^2+2x_1x_2+x_2^2; y_1^2+2y_1y_2+y_2^2$

$\text{II. } x_1^2-2x_1x_2-x_2^2; 2y_1^2+y_1y_2-y_2^2$

$\text{III. } x_1^2+2x_1x_2-2x_2^2; 2y_1^2+y_1y_2+2y_2^2$

$\text{IV. } x_1^2+x_1x_2-x_2^2; y_1^2+y_1y_2-y_2^2$

How many of the above are non-orthogonal pairs?

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