Home
Class 12
MATHS
The locus of the poles of the chords of ...

The locus of the poles of the chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` which subtend a right angle at its centre is

Text Solution

Verified by Experts

The correct Answer is:
`((x^(2))/(a^(2))-(y^(2))/(b^(2)))^(2)((1)/(a^(2))-(1)/(b^(2)))=(x^(2))/(a^(4))+(y^(2))/(b^(4))`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS ENGLISH|Exercise Example|7 Videos

  • HYPERBOLA

    ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Examples : Subjective Type Questions|3 Videos

  • GRAPHICAL TRANSFORMATIONS

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

  • INDEFINITE INTEGRAL

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

Similar Questions

Explore conceptually related problems

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

The locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

The locus of the midpoint of the chords of the hyperbola (x^(2))/(25)-(y^(2))/(36)=1 which passes through the point (2, 4) is a hyperbola, whose transverse axis length (in units) is equal to

If a variable straight line x cos alpha+y sin alpha=p which is a chord of hyperbola (x^(2))/(a^(2))=(y^(2))/(b^(2))=1 (b gt a) subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is (a) (sqrt(a^2+b^2))/(ab) (b) (2ab)/(sqrt(a^2+b^2)) (c) (ab)/(sqrt(b^2-a^2)) (d) (sqrt(a^2+b^2))/(2ab)

The locus of the point of Interection of two tangents to the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 which a make an angle 60^@ with one another is

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (c ,0)dot

The locus of middle points of normal chords of the rectangular hyperbola x^(2)-y^(2)=a^(2) is