Home
Class 12
MATHS
In a rectangular hyperbola, prove that t...

In a rectangular hyperbola, prove that the product of the focal distances of a point on it is equal to the square of its distance from the centre of the hyperbola .

Answer

Step by step text solution for In a rectangular hyperbola, prove that the product of the focal distances of a point on it is equal to the square of its distance from the centre of the hyperbola . by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    FIITJEE|Exercise ASSIGNMENT PROBLEMS ( SUBJECTIVE) Level - I|15 Videos

  • HYPERBOLA

    FIITJEE|Exercise ASSIGNMENT PROBLEMS ( SUBJECTIVE) Level - II|11 Videos

  • HYPERBOLA

    FIITJEE|Exercise Exercise - 2|4 Videos

  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise EXERCISE-8|1 Videos

Similar Questions

Explore conceptually related problems

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

The difference of the focal distances of any point on the hyperbola is equal to its

Knowledge Check

  • The difference of the focal distance of any point on the hyperbola is equal to its

    A
    latusrectum
    B
    eccentricity
    C
    length of the transverse axis
    D
    half the length of the transverse axis

  • The difference of the focal distance of any point on the hyperbola is equal to its

    A
    latusrectum
    B
    eccentricity
    C
    length of the transverse axis
    D
    half the length of the tranverse axis

  • The difference of the focal distance of any point on the hyperbola is equal to its

    A
    Latus rectum
    B
    Eccentricity
    C
    Length of the transverse axis
    D
    Half the length of the transverse axis

    • Similar Questions

    Explore conceptually related problems

    The locus ofthe foot of the perpendicular from the centre of the hyperbola

    Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

    A point p is such that the sum of squares of its distance from the axes of coordinates is equal to the square of its distance from the line x-y=1. Find the locus of P

    Prove that product of parameters of four concyclic points on the hyperbola xy=c^(2) is 1. Also, prove that the mean of these four concyclic points bisects the distance between the centres of the hyperbola and the circle.

    The difference of focal distances of any point on a hyperbola is equal to:

    Home
    Profile