Home
Class 12
MATHS
The locus of the point of intersection o...

The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, is

Text Solution

Verified by Experts

The correct Answer is:
`(a^(6))/(x^(2))-(b^(6))/(y^(2))=(a^(2)+b^(2))^(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE HYPERBOLA

    ML KHANNA|Exercise MISCELLANGEOUS EXERCISE (MATCHING ENTERIES) |1 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise SELF ASSESSMENT TEST |4 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise PROBLEM SET (3) (TRUE AND FALSE) |5 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

Similar Questions

Explore conceptually related problems

The locus of the point of intersection of the tangents at the ends of normal chord of the hyperbola x^(2)-y^(2)=a^(2) is

The locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(b

Knowledge Check

  • The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy = c^(2)

    A
    `(x^(2) - y^(2))^(2) +4c^(2) xy = 0 `
    B
    `(x^(2) + y^(2))^(2) + 4c^(2) xy = 0 `
    C
    `(x^(2) - y^(2))^(2) + 4c xy = 0 `
    D
    `(x^(2) + y^(2))^(2) + 4c xy = 0 `

  • Locus of the intersection of the tangents at the ends of the normal chords of the parabola y^(2) = 4ax is

    A
    `(2a+x)y^(2)+4a^(3)=0`
    B
    `(x+2a)y^(2)+4a^(2)=0`
    C
    `(x+2a)y^(2)+4a=0`
    D
    none

  • Locus of the point of intersection of the tangents at the points with eccentric angles phi and (pi)/(2) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

    A
    `x=a`
    B
    `y=b`
    C
    `x=ab`
    D
    `y=ab`

    • Similar Questions

    Explore conceptually related problems

    Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^(2)-y^(2)=a^(2) is a^(2)(y^(2)-x^(2))=4x^(2)y^(2)

    Find the locus of point of intersection of tangents at the extremities of normal chords of the elipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

    Find the locus of the mid-points of normal chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

    The locus of the point of intersection of tangents at the extremities of the chords of hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 which are tangents to the circle drawn on the line joining the foci as diameter is

    The locus of the point of intersection of tangents at the end-points of conjugate diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

    Home
    Profile