Page 847 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

This reduces to

which in standard form is

Exercise Set 11.1

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Find the equations of the lines that pass through the following points:
1.

(a) (1, −1), (2, 2)

(b) (0, 1), (1, −1)

Find the equations of the circles that pass through the following points:
2.

(a) (2, 6), (2, 0), (5, 3)

(b) (2, −2), (3, 5), (−4, 6)

Find the equation of the conic section that passes through the points (0, 0), (0, −1), (2, 0), (2, −5), and (4, −1).
3.

Find the equations of the planes in 3-space that pass through the following points:
4.

(a) (1, 1, −3), (1, −1, 1), (0, −1, 2)

(b) (2, 3, 1), (2, −1, −1), (1, 2, 1)

5.
(a) Alter Equation 11 so that it determines the plane that passes through the origin and is parallel to the plane that passes
through three specified noncollinear points.