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A hyperbola passes through the point P(s...

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

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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:

A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci at (+-2,0) them the tangent to this hyperbola at P also passes through the point (A)(sqrt(3),sqrt(2))(B)(-sqrt(2),-sqrt(3))(C)(3sqrt(2),2sqrt(3))(D)(2sqrt(2),3sqrt(3))

(3sqrt(2)-sqrt(3))(4sqrt(3)-sqrt(2))

(1)/(sqrt(3)+sqrt(2))-(2)/(sqrt(5)-sqrt(3))-(3)/(sqrt(2)-sqrt(5))

(2sqrt(3)+3sqrt(2))/(3sqrt(2)-2sqrt(3))

(3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(sqrt(12))/(sqrt(3)-sqrt(2))

(sqrt((2)/(5))+sqrt((3)/(3)))(sqrt(2)+sqrt(3))

(1)/(sqrt(2)+sqrt(3))-(2)/(sqrt(5)-sqrt(3))+(3)/(sqrt(5)-sqrt(2))=

Simplify- (3*sqrt(2)-2*sqrt(3))/(3*sqrt(2)+2*sqrt(3))+(sqrt(12))/(sqrt(3)-2)

1/(sqrt(3)+sqrt(2))-2/(sqrt(5)-sqrt(3))-3/(sqrt(2)-sqrt(5))

MCGROW HILL PUBLICATION-HYPERBOLA-QUESTION FROM PREVIOUS YEARS AIEEE/JEE MAIN PAPERS
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  2. The equation of the hyperbola whose foci are (-2, 0) and (2,0) and ecc...

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  3. A tangent to the hyperbola meets x-axis at P and y-axis at Q. Lines P...

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  4. A common tangent to the conics x^2=6y and 2x^2-4y^2=9 is

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  5. If P(3 sec theta,2 tan theta) and Q(3 sec phi , 2 tan phi) where theta...

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  6. The tangent at an extremity (in the first quadrant) of latus rectum of...

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  7. An ellipse passes through the foci of the hyperbola, 9x^2 - 4y^2 = 36 ...

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  8. The eccentricity of the hyperbola whose length of the latus rectum is ...

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  9. A hyperbola whose transverse axis is along the major axis of the conic...

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  10. Let a and b respectively be the semi-transverse and semi-conjugate axe...

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  11. The locus of the point of intersection of thestraight lines tx-2y-3t=...

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

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  13. Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q....

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  14. If the tangent drawn to the hyperbola 4y^2=x^2+1 intersect the co-ordi...

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  15. If a hyperbola has length of its conjugate axis equal to 5 and the dis...

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  16. Equation of a common tangent to the parabola y^(2)=4x and the hyperbol...

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  17. Let 0 lt theta lt (pi)/2. If the eccentricity of the hyperbola (x^(2))...

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  18. The equation of tangent to hyperbola 4x^2-5y^2=20 which is parallel to...

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  19. A hyperbola has its centre at the origin, passes through the point (4,...

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  20. Let S={(x,y) in R^(2):(y^(2))/(1+r)-(x^(2))/(1-r)=1}, where r ne pm 1....

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