Home
Class 12
MATHS
Prove that the perpendicular focal chord...

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.

A

`PQ=RS`

B

`PQ^2+(RS)^2= (" latus rectum ")^2`

C

PQ+RS= (latus rectum)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|178 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

Similar Questions

Explore conceptually related problems

Prove that the eccentricity of a rectangular hyperbola is equal to sqrt2 .

P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot

The eccentricity of a rectangular hyperbola, is

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

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

If angle subtended by any chord of a rectangular hyperbola at the centre is alpha and angle between the tangents at ends of chord is beta , then

The normal PG to a curve meets the x-axis in G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 2
  1. If P(a sec alpha,b tan alpha)" and "Q(a sec beta, b tan beta) are two ...

    Text Solution

    |

  2. If x+iy=sqrt(phi+iy), where i=sqrt(-1)" and "phi and Psi are non-zero ...

    Text Solution

    |

  3. If a ray of light incident along the line 3x+(5-4sqrt2)y=15 gets refle...

    Text Solution

    |

  4. At the point of intersection of the rectangular hyperbola xy = c^(2) a...

    Text Solution

    |

  5. If p ,q ,r ,s ae rational numbers and the roots of f(x)=0 are eccentri...

    Text Solution

    |

  6. If from the point (alpha,alpha^2) two tangents drawn to any one branch...

    Text Solution

    |

  7. Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of ...

    Text Solution

    |

  8. If theta is eliminated from the equations a sec theta-x tan theta=y" a...

    Text Solution

    |

  9. If A hyperbola be rectangular and its equation be xy=c^(2), prove tha...

    Text Solution

    |

  10. The normal at P(ct,(c )/(t)) to the hyperbola xy=c^2 meets it again a...

    Text Solution

    |

  11. Chords of the hyperbola x^2/a^2-y^2/b^2=1 are tangents to the circle d...

    Text Solution

    |

  12. Two rods of lengths aa n db slide along the x- and y-axis , respective...

    Text Solution

    |

  13. Show that the acute angle between the asymptotes of the hyperbola (x^2...

    Text Solution

    |

  14. the product of the perpendicular distance from any points on a hyperbo...

    Text Solution

    |

  15. Prove that the perpendicular focal chords of a rectangular hyperbola a...

    Text Solution

    |

  16. If a variable line has its intercepts on the coordinate axes ea n de^(...

    Text Solution

    |

  17. Tangents are drawn to hyperbola (x^2)/(16)-(y^2)/(b^2)=1. (b being par...

    Text Solution

    |

  18. A straight line through the point (1,1) meets the X-axis at A and Y-ax...

    Text Solution

    |

  19. The line lx + my+n=0 will be a normal to the hyperbola b^2x^2-a^2y^2...

    Text Solution

    |

  20. Prove that the focus of id-points of the portion of the tamgents to th...

    Text Solution

    |