Home
Class 12
MATHS
If the tangent and normal to a rectangul...

If the tangent and normal to a rectangular hyperbola cut off intercepts `a_(1)` and `a_(2)` on one axis and `b_(1)` and `b_(2)` on the other, then

A

`x_1y_1+x_2y_2=0`

B

`x_1y_2+x_2y_1=0`

C

`x_1x_2+y_1y_2=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|15 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise For Session 3|17 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

If the tangent and normal to the rectangular hyperbola xy=16 at point (8,2) cut off intercepts a_(1),a_(2) on the x axis and b_(1)b_(2) on the y axis then a_(1)a_(2)+b_(1)b_(2)+7//2 equals

If the tangent and the normal to a rectangular hyperbola xy = c^(2) , at a point , cuts off intercepts a_(1)" and " a_(2) on the x- axis and b_(1) b_(2) on the y- axis, then a_(1)a_(2) + b_(1) b_(2) is equal to

If the tangent and normal to xy=c^2 at a given point on it cut off intercepts a_1, a_2 on one axis and b_1, b_2 on the other axis, then a_1 a_2 + b_1 b_2 = (A) -1 (B) 1 (C) 0 (D) a_1 a_2 b_1 b_2

If the tangent and normal to the hyperbola x^(2) - y^(2) = 4 at a point cut off intercepts a_(1) and a^(2) respectively on the x-axis, and b_(1) and b_(2) respectively on the y-axis, then the value of a_(1)a_(2) + b_(1)b_(2) is

If the tangent and the normal to x^2-y^2=4 at a point cut off intercepts a_1,a_2 on the x-axis respectively & b_1,b_2 on the y-axis respectively. Then the value of a_1a_2+b_1b_2 is equal to:

If the intercepts made by tangent,normal to a rectangular x^(2)-y^(2)=a^(2) with x -axis are a_(1),a_(2) and with y-axis are b_(1),b_(2) then a_(1),a_(2)+b_(1)b_(2)=

Let a and b be positive real numbers such that a gt 1 and b lt a . Let be a point in the first quadrant that lies on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 . Suppose the tangent to the hyperbola at P passes through the oint (1,0) and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes . Let Delta denote the area of the triangle formed by the tangent at P , the normal at P and the x - axis . If a denotes the eccentricity of the hyperbola , then which of the following statements is/are TRUE ?

If vec P = a_(1) hati +a_(2) hatj and vec Q =b_(1) hati+b_(2)hatj are perpendicular to each other, then

If the equation of the locus of a point equidistant from the points (a_(1),b_(1)) and (a_(2),b_(2)) is (a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0 then the value of c is

ARIHANT MATHS-HYPERBOLA-Exercise (Single Option Correct Type Questions)
  1. Let A=(-3, 4) and B=(2, -1) be two fixed points. A point C moves such ...

    Text Solution

    |

  2. A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-...

    Text Solution

    |

  3. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

    Text Solution

    |

  4. If alpha+beta=3pi , then the chord joining the points alpha and beta f...

    Text Solution

    |

  5. If x^2/a^2+y^2/b^2=1(a>b) and x^2-y^2=c^2 cut at right angles, then:

    Text Solution

    |

  6. Chords of the hyperbola, x^2-y^2 = a^2 touch the parabola, y^2 = 4ax. ...

    Text Solution

    |

  7. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

    Text Solution

    |

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

    Text Solution

    |

  9. The condition that a straight line with slope m will be normal to para...

    Text Solution

    |

  10. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

    Text Solution

    |

  11. The co-ordinates of the centre of the hyperbola, x^2+3x y+3y^2+2x+3y+2...

    Text Solution

    |

  12. Let F1,F2 are the foci of the hyperbola x^2/16-y^2/9=1 and F3,F4 are t...

    Text Solution

    |

  13. Locus of the point of intersection of the tangents at the points with ...

    Text Solution

    |

  14. Latusrectum of the conic satisfying the differential equation xdy+ydx=...

    Text Solution

    |

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

    Text Solution

    |

  16. If the tangent and normal to a rectangular hyperbola cut off intercept...

    Text Solution

    |

  17. The focus of rectangular hyperbola (x-a)*(y-b)=c^2 is

    Text Solution

    |

  18. The equation of a hyperbola conjugate to the hyperbola x^(2)+3xy+2y^(2...

    Text Solution

    |

  19. If values of a, for which the line y=ax+2sqrt(5) touches the hyperbola...

    Text Solution

    |

  20. Let C be a curve which is the locus of the point of intersection of li...

    Text Solution

    |