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Find the point on the hyperbola x^2/24 -...

Find the point on the hyperbola `x^2/24 - y^2/18 = 1` which is nearest to the line `3x+2y+1=0` and compute the distance between the point and the line.

A

`(6, 3)`

B

`(-6, 3)`

C

`(6, -3)`

D

`(-6, -3)`

Text Solution

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The correct Answer is:
b
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FIITJEE-HYPERBOLA-SOLVED PROBLEMES (OBJECTIVE)
  1. The locus of the midde points ofchords of hyperbola 3x^2-2y^2+4x -6y=0...

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  2. The line lx + my+n=0 will be a normal to the hyperbola b^2x^2-a^2y^2...

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  3. Find the point on the hyperbola x^2/24 - y^2/18 = 1 which is nearest t...

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  4. For a hyperbola, the foci are at (pm 4, 0) and vertices at (pm 2 , 0) ...

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  5. The equation of the line passing through the centre of a rectangular h...

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  6. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 me...

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  7. The point of intersection of the curve whose parametrix equations are ...

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  8. If a rectangular hyperbola (x-1)(y-2)=4 cuts a circle x^(2)+y^(2)+2gx+...

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  9. The equation (x-alpha)^2+(y-beta)^2=k(lx+my+n)^2 represents

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  10. The angle between the hyperbola xy = c^(2) " and " x^(2) - y^(2) = a^(...

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  11. If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the fo...

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  12. The equation 16x^(2) - 3y^(2) - 32x - 12y - 44 = 0 represents a hyper...

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  13. Locus of mid point of AB is

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  14. If the eccentric angle of point on the hyperbola where the common tang...

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  15. If the eccentric angle of the point of contact of common tangent on th...

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  16. Angle subtended by AB at centre the hyperbola is

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  17. Let xy - 2x - y + 2 = 0 are the asymptotes of a hyperbola H, passing ...

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  18. If four points be taken on a rectangular hyperbola such that the chord...

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  19. Let the normals are drawn (alpha, beta ) to the hyperbola xy = 1 " and...

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  20. Combined equation of pair of tangent to the hyperbola x^(2) - y^(2) = ...

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