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A hyperbola passes through the point `P(sqrt(2),sqrt(3))` and has foci at `(+-2,0)dot` Then the tangent to this hyperbola at `P` also passes through the point : `(sqrt(3),sqrt(2))` (2) `(-sqrt(2),-sqrt(3))` (3) `(3sqrt(2),2sqrt(3))` (4) `(2sqrt(2),3sqrt(3)`

A

`(-sqrt(2), -sqrt(3))`

B

`(3sqrt(2), 2sqrt(3))`

C

`(2sqrt(2), 3sqrt(3))`

D

`(sqrt(3), sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci at (+-2,0). Then the tangent to this hyperbola at P also passes through the point:

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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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