8 The circle C has equation x' + y -18x - 6y + 45 = 0 a. Find the radius of C and the coordinates of its centre P. b. Show that the line y = 2x is a tangent to C and find the coordinates of its point of contactQ. c. Show that the tangent to C at the point R(6, 9) has equation x- 2y +12 = 0 d. Given that the tangents to C at Q and R meet at S show that QS = V5. %3D

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
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8 The circle C has equation x² + y -18x – 6y+ 45 = 0
a. Find the radius of C and the coordinates of its centre P.
b. Show that the line y = 2x is a tangent to C and find the coordinates of its point of contactQ.
c. Show that the tangent to C at the point R(6, 9) has equation x - 2y +12 = 0
d. Given that the tangents to C at Q and R meet at S show that QS = V5.
Transcribed Image Text:8 The circle C has equation x² + y -18x – 6y+ 45 = 0 a. Find the radius of C and the coordinates of its centre P. b. Show that the line y = 2x is a tangent to C and find the coordinates of its point of contactQ. c. Show that the tangent to C at the point R(6, 9) has equation x - 2y +12 = 0 d. Given that the tangents to C at Q and R meet at S show that QS = V5.
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