The line with equation y = kx intersects the circle with equation x 2 10x +

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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 decimal places.

a. Show that 21k2 − 60k + 32 < 0.

b. Hence determine the range of possible values for k.

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