If | ab | = 4, then such a line L has () A. 1 B. 2 C. 3 d. 4 | Math enthusiast | Mathematical art

If | ab | = 4, then such a line L has () A. 1 B. 2 C. 3 d. 4

∵ the distance between the two vertices of the hyperbola is 2, less than 4, ∵ when there is an intersection between the straight line and the left and right branches of the hyperbola, there must be two straight lines passing through the focus of the hyperbola, so that the distance between the two intersections is equal to 4. When the straight line is perpendicular to the real axis, there is 3-y22 = 1, and the solution is y = ± 2, ∵ at this time, the length of the straight line AB is 4, that is, there is only one line with chord length of 4 which has an intersection with the right branch In conclusion, there are three straight lines satisfying | ab | = 4, so C

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