Home
Class 12
MATHS
For which of the hyperbolas, can we have...

For which of the hyperbolas, can we have more than one pair of perpendicular tangents? (a)`(x^2)/4-(y^2)/9=1` (b) `(x^2)/4-(y^2)/9=-1` (c)`x^2-y^2=4` (d) `x y=44`

A

`(x^(2))/(4)-(y^(2))/(9)=1`

B

`(x^(2))/(4)-(y^(2))/(9)=-1`

C

`x^(2)-y^(2)=4`

D

`xy=44`

Text Solution

Verified by Experts

The correct Answer is:
B
The locus of the point of intersection of perpendicular tangents is director circle for
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
The equation of director circle is `x^(2)+y^(2)=a^(2)-b^(2)`which is real if a gt b.
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Comprehension)|21 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Single)|68 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

The locus of the point of intersection of perpendicular tangents to the hyperbola x^(2)/16 - y^(2)/9 = 1 is _____

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (x^2-y^2)=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be (a) x^2+y^2=6 (b) x^2+y^2=9 (c) x^2+y^2=3 (d) x^2+y^2=18

If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equation of the corresponding pair of tangents is (A) 9x^2-8y^2+18x-9=0 (B) 9x^2-8y^2-18x+9=0 (C) 9x^2-8y^2-18x-9=0 (D) 9x^2-8y^2+18x+9=0

If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the midpoint of the intercept made by the tangents between the coordinate axes is (a) 1/(2x^2)+1/(4y^2)=1 (b) 1/(4x^2)+1/(2y^2)=1 (c) (x^2)/2+y^2=1 (d) (x^2)/4+(y^2)/2=1

The mirror image of the parabola y^2=4x in the tangent to the parabola at the point (1, 2) is (a) (x-1)^2=4(y+1) (b) (x+1)^2=4(y+1) (c) (x+1)^2=4(y-1) (d) (x-1)^2=4(y-1)

The locus of the foot of the perpendicular from the centre of the hyperbola xy = c^2 on a variable tangent is (A) (x^2-y^2)=4c^2xy (B) (x^2+y^2)^2=2c^2xy (C) (x^2+y^2)=4c^2xy (D) (x^2+y^2)^2=4c^2xy

The equation of the line that passes through (10 ,-1) and is perpendicular to y=(x^2)/4-2 is (a)4x+y=39 (b) 2x+y=19 (c)x+y=9 (d) x+2y=8

The number of points on the ellipse (x^2)/(50)+(y^2)/(20)=1 from which a pair of perpendicular tangents is drawn to the ellipse (x^2)/(16)+(y^2)/9=1 is (a)0 (b) 2 (c) 1 (d) 4

Which of the following can be slope of tangent to the hyperbola 4x^2-y^2=4? (a)1 (b) -3 (c) 2 (d) -3/2

CENGAGE-HYPERBOLA-Exercise (Multiple)
  1. If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four poi...

    Text Solution

    |

  2. The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents a parabo...

    Text Solution

    |

  3. If (5,12)a n d(24 ,7) are the foci of a hyperbola passing through the ...

    Text Solution

    |

  4. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

    Text Solution

    |

  5. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

    Text Solution

    |

  6. If the foci of (x^2)/(a^2)-(y^2)/(b^2)=1 coincide with the foci of (x^...

    Text Solution

    |

  7. The differential equation (dy)/(dx)=(3y)/(2x) represents a family of h...

    Text Solution

    |

  8. The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that...

    Text Solution

    |

  9. A parabola is drawn with focus at one of the foci of the ellipse (x^2)...

    Text Solution

    |

  10. For which of the hyperbolas, can we have more than one pair of perpe...

    Text Solution

    |

  11. The lines parallel to the normal to the curve x y=1 is/are (a)3x+4y+5=...

    Text Solution

    |

  12. From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y...

    Text Solution

    |

  13. For the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , let n be the number of p...

    Text Solution

    |

  14. If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the ax...

    Text Solution

    |

  15. Find the equation of tangent to the hyperbola y=(x+9)/(x+5) which pas...

    Text Solution

    |

  16. Tangents which are parrallel to the line 2x+y+8=0 are drawn to hyperb...

    Text Solution

    |

  17. Find the equations of the tangents to the hyperbola x^2=9y^2=9 that ar...

    Text Solution

    |

  18. Circle are drawn on the chords of the rectangular hyperbola x y=4 para...

    Text Solution

    |