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11 Nov 2019
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(a.) Find the two points of intersection of the line y = -2x + 1and the circle of radius 1 with center (0,0).
(b.) Find the two points of intersection of the line y = 4x + 1and the circle of radius 1 with center (0,0).
(c.) Suppose m is a (non-zero) rational number and we intersectthe line defined by y = mx + 1 with the unit circle C centered atthe origin. Explain why (0,1) is one solution and the othersolution has rational numbers for both coordinates.
(d.) Parts (a.), (b.),and (c.) produce a point on C differentfrom (1,0). Explain how this point can be used to produce aPythagorean triple.
Show all your work
(a.) Find the two points of intersection of the line y = -2x + 1and the circle of radius 1 with center (0,0).
(b.) Find the two points of intersection of the line y = 4x + 1and the circle of radius 1 with center (0,0).
(c.) Suppose m is a (non-zero) rational number and we intersectthe line defined by y = mx + 1 with the unit circle C centered atthe origin. Explain why (0,1) is one solution and the othersolution has rational numbers for both coordinates.
(d.) Parts (a.), (b.),and (c.) produce a point on C differentfrom (1,0). Explain how this point can be used to produce aPythagorean triple.
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Collen VonLv2
8 Feb 2019