1) Using the manipulate tool set = 0º and A=4. This makes the equation of the cone: (z −4)² = x² + y² What conic section is produced with the intersection of the cone and the x-y plane? 2) Find the equation of the conic section in the x-y plane by setting z = 0 and putting the equation in standard form for conic sections. Write down the equation below. 3) Parameterize your equation from 2) by setting x = t and solve for y. Write down the formula you found for y(t) below.

1) Using the manipulate tool set = 0º and A=4. This makes the equation of the cone: (z −4)² = x² + y² What conic section is produced with the intersection of the cone and the x-y plane? 2) Find the equation of the conic section in the x-y plane by setting z = 0 and putting the equation in standard form for conic sections. Write down the equation below. 3) Parameterize your equation from 2) by setting x = t and solve for y. Write down the formula you found for y(t) below.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 34E

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Question

Please answer the following parts: 1.What conic section is produced? 2. How do you find the equation of the conic section? 3.How do you parameterize the equation of the conic section? 4. What is the domain for y(t)?

1) Using the manipulate tool set = 0º and A=4. This makes the equation of the cone:
(z −4)² = x² + y²
What conic section is produced with the intersection of the cone and the x-y plane?
2) Find the equation of the conic section in the x-y plane by setting z = 0 and putting the equation
in standard form for conic sections. Write down the equation below.
3) Parameterize your equation from 2) by setting x = t and solve for y. Write down the formula you
found for y(t) below.
4) What is the domain for y(t)? The domain for y(t) will determine tmin and Imax in part 5)

Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.

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