1.

Consider a hyperbola: ((x-7)^(2))/(a) -((y+3)^(2))/(b^(2)) =1. The line 3x - 2y - 25 =0, which is not a tangent, intersect the hyperbola at H ((11)/(3),-7) only. A variable point P(alpha +7, alpha^(2)-4) AA alpha in R exists in the plane of the given hyperbola. The eccentricity of the hyperbola is

Answer»

`sqrt((7)/(5))`
`sqrt(2)`
`(sqrt(13))/(2)`
`(3)/(2)`

Solution :The GIVEN line must be PARALLEL to asymptotes
`rArr` SLOPE of asymptotes are `(3)/(2)` and `-(3)/(2)`
`rArr (b)/(a) =(3)/(2) rArr e = (sqrt(13))/(2)`


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