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Let a hyperbola passes through the focus of the ellipse `(x^(2))/(25)+(y^(2))/(16)=1`. The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse, also the product of eccentricities of given ellipse and hyperbola is 1, then

A

the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(16)=1`

B

the equation of hyperbola is `(x^(2))/(9)-(y^(2))/(25)=1`

C

focus of hyperbola is `(5, 0)`

D

vertex of hyperbola is `(5sqrt(3), 0)`

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The correct Answer is:
A, C
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ARIHANT MATHS-HYPERBOLA-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(...

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  3. A hyperbola, having the transverse axis of length 2sin theta, is conf...

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  4. Two braches of a hyperbola

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  5. For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of ...

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  6. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

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  7. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

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  8. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

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  9. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

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  10. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

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  11. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

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  12. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

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  13. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

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  14. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

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  15. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

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  16. A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci a...

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  17. If 2x-y+1=0 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(16)=1 the...

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