As shown in the figure, it is known that the image of inverse scale function y = KX passes through point C (- 3,8), and the image of primary function passes through point C and intersects with X axis and Y axis at points a and B respectively, if OA = 3 and ab = BC. (1) find the analytic expression of inverse scale function; (2) find the length of AC and ob

As shown in the figure, it is known that the image of inverse scale function y = KX passes through point C (- 3,8), and the image of primary function passes through point C and intersects with X axis and Y axis at points a and B respectively, if OA = 3 and ab = BC. (1) find the analytic expression of inverse scale function; (2) find the length of AC and ob

(1) According to the meaning of the question, we can get: 8 = k − 3 (2 points) ∧ k = - 24. (3 points) ∧ the analytic formula of inverse proportional function y = − 24x. (4 points) (2) through point C as CE ⊥ X axis, the perpendicular foot is E (5 points) from C (- 3,8), we can see OE = OA = 3, ∧ AE = Ao + OE = 6, CE = 8, ∧ AC | = AE2 + CE2 = 62 + 82 = 10 (10 points), ab = BC, OE = OA, ∧ ob = 12ce = 4. (13 points)