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Find the Equation of the Hyperbola Whose Foci Are `(0,+- Sqrt10)` and Passing Through the Point (2,3) - ISC (Science) Class 12 - Mathematics

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Question

Find the equation of the hyperbola whose foci are `(0,+- sqrt10)` and passing through the point (2,3)

Solution

`foci -> (0, +- sqrt10)`

be = `sqrt10` ......(1)

Equation of hyperbola is

`y^2/b^2 - x^2/a^2 = 1`  .......(2)

equation 2 passing through (2, 3)

`:. 9/b^2 - 4/a^2 = 1`

we know that `a^2 = b^2e^2 - b^2`

`a^2 = 10 -  b^2`

`9/b^2 - 4/(10 - b^2) = 1`

Put `b^2 = t`

`9/t- 4/(10 - t) = 1`

`90 - 9t - 4t = 10t - t^2`

`t^2 - 23t  + 90 = 0`

t = 18, t = 5

`b^2 = 18, b^2 = 5`

`b = 3sqrt2 , b =  sqrt5`

When `b = 3sqrt2`

then `a^2 = 10 - 18 = -8`   (Neglected `∵ a = sqrt-8` is an imaginary number).

∴ when `b =  sqrt5`

then `a =  sqrt5`

∴ equation of hyperbola

`y^2/5 - x^2/5  = 1`

`y^2 - x^2 = 5`

  Is there an error in this question or solution?

APPEARS IN

 2014-2015 (March) (with solutions)
Question 4.2 | 5.00 marks
Solution Find the Equation of the Hyperbola Whose Foci Are `(0,+- Sqrt10)` and Passing Through the Point (2,3) Concept: Solve Population Based Problems on Application of Differential Equations.
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