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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

ConceptSolve Population Based Problems on Application of Differential Equations

#### 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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