JEE Maths - Hyperbola

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Question - 1

Consider the set of hyperbola xy = 1, k \(\epsilon\) R. Let e1 be the eccentricity when k = 4 and e2 be the eccentricity when k = 9 then e1 - e2 = ______________

  • A 4.00
  • B 6.00
  • C 9.00
  • D 0.00

Question - 2

If the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{b^{2}}=1\) and the hyperbola \(\frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25}\)coincide, then find the value of b2

  • A 14
  • B 17
  • C 15
  • D 16

Question - 3

Find the eccentricity of the conjugate hyperbola of the hyperbola x2 - 3y2 = 1

  • A 4
  • B 5
  • C 3
  • D 2

Question - 4

A tangent drawn to hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \text { at } P\left(\frac{\pi}{6}\right)\) forms a triangle of area 3a2 square units, with coordinate axes, then the square of its eccentricity.

  • A 19
  • B 20
  • C 18
  • D 17

Question - 5

Find the eccentricity of the hyperbola \(\frac{\sqrt{1999}}{3}\left(x^{2}-y^{2}\right)=1\).

  • A 1.876
  • B 2.456
  • C 1.475
  • D 1.414

Question - 6

Find the eccentricity of the hyperbola whose latus rectum 12 and semi-conjugate axis is 2\(\sqrt3\)

  • A 0
  • B 8
  • C 5
  • D 2

Question - 7

If the eccentricity and length of latus rectum of a hyperbola are \(\frac{\sqrt{13}}{3} \text { and } \frac{10}{3}\) units respectively, then find the length of the transverse axis.

  • A 5.50
  • B 4.50
  • C 6.50
  • D 7.50

Question - 8

If P is any point on the hyperbola \(\frac{(x-1)^{2}}{9}-\frac{(y+1)^{2}}{16}=1\)and S1 and S2 are its foci then find value of |S1P-S2P|.

  • A 8.00
  • B 9.00
  • C 7.00
  • D 6.00

Question - 9

The straight line x +y =\(\sqrt2\) p touches the hyperbola 4x2 + 9y2 = 36, then findvalue of p2

  • A 4.50
  • B 5.00
  • C 3.50
  • D 2.50

Question - 10

If e and e' are the eccentricities of the ellipse 5x2 + 9y2 - 45 and the hyperbola 5x2- 4y2 - 4b respectively, then find value of ee'.

  • A 3.00
  • B 4.00
  • C 2.00
  • D 1.00
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