Given the circles Cx2 + y² – 6x – 4y + 9 = 0 and C2:x² + y2 - 2x- 6y + 9 = 0, Find, (a) the equation of the circle C3 which passes through the centre of C,and through the point of intersection of C,and C2. (b) the equations of the two tangents from the origin to C, and the length of each tangent.

Given the circles Cx2 + y² – 6x – 4y + 9 = 0 and C2:x² + y2 - 2x- 6y + 9 = 0, Find, (a) the equation of the circle C3 which passes through the centre of C,and through the point of intersection of C,and C2. (b) the equations of the two tangents from the origin to C, and the length of each tangent.

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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Question

Given the circles C:x2 + y² – 6x – 4y +9 = 0 and C2:x² + y? – 2x – 6y + 9 = 0,
Find,
(a) the equation of the circle C3 which passes through the centre of C,and through the point of
intersection of C, and C2.
(b) the equations of the two tangents from the origin to C, and the length of each tangent.

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