3. Let C be the conic with equation:y² + 8y - 8x = 8.(a) Find the discriminant of C and hence determine what kind of conic C is.(b) Determine each of the following features of C (where they exist): eccentricity,centre, vertices, foci, directrices, asymptotes, axis intercepts.(c) Give a sketch of C including the features (except eccentricity) found in part (b).(d) Let C' be the conic with equation:y² + 8y + 8x = 8.Find all points lying on both C and C'.(e) Find examples of straight lines which intersect C in:(i) exactly two points;(ii) exactly one point;(iii) no points,

Note: It is a multipart question. No specific part has been asked.So, we will solve the first three…

Answered: 3. Let C be the conic with equation: y²…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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24) Find the vertices and foci of the conic and sketch the graph: 4x² + y² +8x−4y−8=0 25) Find all points of vertical and horizontal tangents to the parametric curve: x=t³-3t, y=t² +4t+3
Please do the following handwritten
4. Find the a) eccentricity, b) identify the conic, c) sketch the conic that corresponds to the focus at the origin. 4 Label the vertices with the appropriate polar coordinates. r = Label the vertices, foci, directrices, and 2+3 cos e asymptotes (if they exist). Use the polar graph attached to graph.
8. Use the following conic sections to answer: x2 – 2x + 2y2 – 8y + 7 = 0 a. Graph the conic section b. Give the key features of the conic section (e.g. center, vertex, asymptotes, eccentricity, etc.) c. Transform the conic section into polar. Make sure you simplify to r=equation.
Find the equation of the conic described
Consider the conic section given by the polar equation 4 1-sin 0 (a) (b) (c) (d) r = Without converting into Cartesian form, identify the conic section represented by the equation above. Write out, with justification, the directrix and the focus (or foci) of the conic section. Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain whether the tangent of the curve at the point where 0 = π/4 is orthog- onal to the line y = √2x+1.
Classify the following equations of conics indicating their centers or vertices. (Conic: Circumference, parabola, ellipse and hyperbola) a) 2x2 + 2y2 – 4x + 4y + 2 = 0. b) 8x2 – 3y2 = 120. c) y = x2 – 2x + 3. d) x = –3y2 + y + 5.
Consider the conic section given by the polar equation 4 1-sin 0 (a) (b) (c) (d) r = Without converting into Cartesian form, identify the conic section represented by the equation above. Write out, with justification, the directrix and the focus (or foci) of the conic section. Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain whether the tangent of the curve at the point where 0 = π/4 is orthog- onal to the line y = √√2x+1.

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