Q. 7 A4.3( 4 Votes )

Find the equation

Answer :

Given: Foci are (6, 4) and (-4, 4) and eccentricity is 2


To find: equation of the hyperbola


Formula used:


The standard form of the equation of the hyperbola is,



Center is the mid-point of two foci.


Distance between the foci is 2ae and b2 = a2(e2 – 1)


The distance between two points (m, n) and (a, b) is given by


Mid-point theorem:


Mid-point of two points (m, n) and (a, b) is given by



Center of hyperbola having foci (6, 4) and (-4, 4) is given by




= (1, 4)


The distance between the foci is 2ae, and Foci are (6, 4) and (-4, 4)








{ e = 2}





b2 = a2(e2 – 1)






The equation of hyperbola:







12(x2 + 1 – 2x) – 4(y2 + 16 – 8y) = 75


12x2 + 12 – 24x – 4y2 – 64 + 32y – 75 = 0


12x2 – 4y2 – 24x + 32y – 127 = 0


Hence, required equation of hyperbola is 12x2 – 4y2 – 24x + 32y – 127 = 0


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