A parametric representation of the curve of intersection of the two surfacesx2 + 5y2 - z = 0 and z - 4y2 = 36 is given by the vector equation :r (t) = 6cosh(t) i+ 2sinh(t) j + (36 - 16 sin²(t) ) K ,0sts 2nr (t) = 6cos(t) i + 2sin(t) j + (36 - 16 sin2(t) ) k , 0 st s 2n= cos(t) i + sin(t) j' + (36 - 16 sin²(t) ) k ,0 st s 2n%3Dr (t) = 6cos(t) i + 6sin(t) j + 36(1 + 4 sin2(t) ) k ,O st s 2nr (t) = cos(t) i + 3sin(t) j + 36cos2(t) k ,0 st s 2A

The given curves are: x2+5y2-z=0 & z=4y2+36 ⇒x2+5y2-(36+4y2)=0⇒x2+y2-36=0⇒x2+y2=36

A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z - 4y2 = 36 is given by the vector equation : r (t) = 6cosh(t) i + 2sinh(t) j + (36 - 16 sin2(t) ) K ,O st s 2n r (t) = 6cos(t) i + 2sin(t) j + (36 - 16 sin2(t) ) K ,O sts 2n r (t) = cos(t) i + sin(t) j + (36 - 16 sin2(t) ) K ,0 st s 2n r (t) = 6cos(t) i + 6sin(t) j + 36(1 + 4 sin2(t) ) k , 0 s t < 2n r (t) = cos(t) i + 3sin(t) j + 36cos2(t) k , 0

A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z - 4y2 = 36 is given by the vector equation : r (t) = 6cosh(t) i + 2sinh(t) j + (36 - 16 sin2(t) ) K ,O st s 2n r (t) = 6cos(t) i + 2sin(t) j + (36 - 16 sin2(t) ) K ,O sts 2n r (t) = cos(t) i + sin(t) j + (36 - 16 sin2(t) ) K ,0 st s 2n r (t) = 6cos(t) i + 6sin(t) j + 36(1 + 4 sin2(t) ) k , 0 s t < 2n r (t) = cos(t) i + 3sin(t) j + 36cos2(t) k , 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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