4. (a) Suppose a pair of axes x and y is rotated by a to obtain a new pair of axes, Xand Y. Show that x = X cos a - - Y sin a and y = X sin a + Y cos a.(b) Let C be the conic section with equation3x² - 2√3xy + y² + 16x + 16√3y = 0.(i) Find a value of a € [0, π) such that the coefficient of XY in the equation forC in X and Y coordinates (as in part (a)) is zero. Find this equation.(ii) Sketch C in the x and y coordinates. Find its eccentricity and (where theseexist) its foci, axis-intercepts, and asymptotes.

Answered: Image /qna-images/answer/298ba45b-d84b-4492-bbbd-f1e1950aab7b.jpg

Answered: 4. (a) Suppose a pair of axes x and y…

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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