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maths circle question help

The line with equation y = kx intersects the circle with equation x² - 10x + y² - 12y + 57 = 0 at two distinct points. Find a range of possible values of k. Round your answer to 2.d.p.
a) Show that 21k² - 60k + 32 < 0.
b) Hence determine the range of possible values for k.

(edited 4 years ago)

Go for it.

Original post by RDKGames

Go for it.

? i'm asking for help :frown:

Reply 3

ghostwalker

Original post by RecallVelocity

? i'm asking for help :frown:

Then please check the maths forum posting guidelines - sticky thread at top of forum.

What have you done, where are you stuck?

Reply 4

diana_rita

Original post by RecallVelocity

This could be wrong but as a starting point for part a, I think you get the second equation and substitute all values of y with 'kx' so x^2 - 10x + (kx)^2 - 12kx + 57 = 0

Reply 5

Physics Enemy

Original post by RecallVelocity

y = kx intersects x² - 10x + y² - 12y + 57 = 0 at two points.
a) Show 21k² - 60k + 32 < 0.
b) Hence determine range of possible k values

So x^2 - 10x + k^2x^2 - 12kx + 57 = 0
(1 + k^2)x^2 - 2(5 + 6k)x + 57 = 0
For inequality in k: note 2 real roots => discrim > 0
Should get their inequality in a), then solve it