Find the equation of the hyperbola whose two foci are S(6,4) and S' (-4,4) and eccentricity is 2.

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We haveS6,4 and S'-4,4 and e=2Slope of SS'=4-4-4-6=0-10=0As slope of hyperbola is 0, hence axis of hyperbola is parallel to X-axis.Equation of parabola will axis parallel to X-axis is given byx-h2a2-y-k2b2=1, where h,k is the center of hyperbola.We know thatSS'=2ae-4-62+4-42=4a4a=1004a=10a=52a2=254We know thatb2=a2e2-1=2544-1=754Mid point of S and S' will give center of hyperbola.h,k=6-42,4+42=1,4Putting all values in equation x-h2a2-y-k2b2=1, we get:x-12254-y-42754=14x-1225-4y-4275=1x-1225-y-4275=14

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