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A point moves on a plane in such a manne...

A point moves on a plane in such a manner that the difference of distance from (3,0) is `(3)/(2)` times its distance from the line 3x - 4 = 0 , Show that the locus of the moving point is a hyperbola and the equation of its locus is `5x^(2) - 4y^(2) = 20`.

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