Obtain The Equation Of A Hyperbola With Coordinate Axes As Principal Axes Given That The Distance Of One Of Its Vertices From The Foci Are 9 And 1 Units.

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Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distance of one of its vertices from the foci are 9 and 1 units.


Correct option is

If vertices are A(a, 0) and A’(–a, 0) and foci are S’(–ae, 0)

Given  l (S’A) = 9 and l (SA) = 1

⇒        a + ae = 9 and ae – a = 1

Or     a(1 + e) = 9 and or a(e – 1) = 1


∴             a(1 + e) = 9


⇒         a = 4

           b2 = a2(e2 – 1)


∴         b2 = 9

From (1), equation of hyperbola is





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