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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).

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).

Elementary Geometry For College Students, 7e
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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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,
Transcribed Image Text: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,
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