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The locus of the point of intersection o...

The locus of the point of intersection of the lines `sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0` (where t is a parameter) is a hyperbola whose eccentricity is: (a)`sqrt3` (b) 2 (c)`2/sqrt3` (d) `4/3`

A

`sqrt3`

B

2

C

`2//sqrt3`

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
B
Eliminating from the given two equations, we have
`(x^(2))/(16)-(y^(2))/(48)=1`
whose eccentricity is
`e=sqrt(1+(48)/(16))=2`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. Let L L ' be the latus rectum through the focus of the hyperbola (x^2)...

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  2. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

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  3. The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 ...

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  4. lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3...

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  5. The equation of the transvers and conjugate axes of a hyperbola are, ...

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  6. Factorise the expression: (x^2–2xy+y^2)–z^2

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  7. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

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  8. The angle between the lines joining the origin to the points of inters...

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  9. A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), s...

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  10. If the distance between two parallel tangents having slope m drawn to ...

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  11. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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  12. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

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  13. The number of roots of the equation x^2+5x+6=0 is

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  14. The locus of a point whose chord of contact with respect to the circle...

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  15. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

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  16. The number of possible tangents which can be drawn to the curve 4x^2-9...

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

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  18. Locus of the feet of the perpendiculars drawn from either foci on a va...

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  19. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

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  20. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

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