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Urgent Help On Question Please! Have My C1 Exam Tommorrow

ok i've just gone through the jan 2009 past paper and i found it quite easy, i got all the questions done until the last one.. a one that involved 'k' i don't know but for some reason the k gets me so confused! anyway the question that i need help on is:

okay the equation of the circle is :
x^2 + y^2 - 6x + 10y + 9 =0
for d(i) i know you have to substitute y=kx in the circle --> x^2+(kx)^2-6x+10(kx)+9=0 . . . but i don't know what to do next

(d) (i) A line has equation y = kx . Show that the x-coordinates of any points of
intersection of the line and the circle satisfy the equation
(k^2 +1)x^2 + 2(5k-3)x + 9 = 0 (2 marks)
(ii) Find the values of k for which the equation
(k^2 +1)x^2 + 2(5k-3)x + 9 = 0
has equal roots. (5 marks)
(iii) Describe the geometrical relationship between the line and the circle when k takes
either of the values found in part (d)(ii).

THANK YOU!! :smile:

Reply 1

insparato

You've basically done d) i) you just need to simplify the answer you get, collecting the terms up and factorising.

ii) a question about roots and quadratics should scream out a word, (discriminant)

iii) Think about what ii) means if the intersection between a line and circle has only one root.