It is known that the equation of hyperbola is X-Y / 3 = 1. A straight line passing through the right focus of hyperbola with a slope of K intersects hyperbola at two points a and B, and OA ⊥ ob is used to find K

C ^ 2 = a ^ 2 + B ^ 2 = 1 + 3 = 4, C = 2, that is, the right focus coordinate is (2,0) the linear equation is y = K (X-2) substituted into the curve equation: x ^ 2 - [K (x-3)] ^ 2 / 3 = 13X ^ 2-k ^ 2 (x ^ 2-6x + 9) = 3 (3-K ^ 2) x ^ 2 + 6K ^ 2x-9k ^ 2-3 = 0x1 + x2 = 6K ^ 2 / (k ^ 2-3) x1x2 = - 3 (3K ^ 2 + 1) / (3-K ^ 2) y1y2 = k ^ 2 (x1-2) (x2-2) = k ^ 2 [

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