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2. (a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors which are parallel to the plane. (b) Find parametric equations for two circles C₁ and C₂ in space such that C and C₂ have the same radius; C and C₂ intersect at the points P(2,-1,3) and Q(2, 1, 3) and nowhere else.

2. (a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors which are parallel to the plane. (b) Find parametric equations for two circles C₁ and C₂ in space such that C and C₂ have the same radius; C and C₂ intersect at the points P(2,-1,3) and Q(2, 1, 3) and nowhere else.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 36E
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2. (a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors which are parallel to the plane. (b) Find parametric equations for two circles C₁ and C₂ in space such that • C₁ and C₂ have the same radius: . C₁ and C₂ intersect at the points P(2,-1,3) and Q(2, 1, 3) and nowhere else.
Transcribed Image Text:2. (a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors which are parallel to the plane. (b) Find parametric equations for two circles C₁ and C₂ in space such that • C₁ and C₂ have the same radius: . C₁ and C₂ intersect at the points P(2,-1,3) and Q(2, 1, 3) and nowhere else.
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