Home
Class 12
MATHS
Any tangent to an ellips (x^(2))/(a^(2))...

Any tangent to an ellips `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, (a gt b)` cut by the tangents at the end points of major axis is T and T' . Prove that the length of intercept of the major axis cut by the circle describe on T T' as diameter is constant and equal to `2sqrt(a^(2)-b^(2))`.

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELLIPSE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)|47 Videos

  • ELLIPSE

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

  • ELLIPSE

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

  • DETERMINANT

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • FUNCTION

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) Equation of the circle described on major axis as diameter is

A tangent to the ellipse 4x^(2)+9y^(2)=36 is cut by the tangent at the extremities of the major axis at T and T^(1), the circle on TT^(1) as diameter passes through the point

Knowledge Check

  • If tangent at any point P on the ellipse 7x^(2) + 16y^(2) = 12 cuts the tangent at the end points of the major axis at the points A and B, then the circle with AB as diameter passes through a fixed point whose coordinates are

    A
    `(pmsqrt(a^(2)-b^(2)),0)`
    B
    `(pmsqrt(a^(2)+b^(2)),0)`
    C
    `(0,pmsqrt(a^(2)-b^(2)))`
    D
    `(0,sqrt(a^(2)+b^(2)))`

  • If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the normal at an end of a latusrectum cuts the major axis in G, then CG =

    A
    ae
    B
    `a^(2) e^(2)`
    C
    `ae^(3)`
    D
    `a^(2) e^(3)`

  • The tangent at any point on the ellipse 16x^(2)+25y^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

    A
    `(3,0)`
    B
    `(0,0)`
    C
    `(0,3)`
    D
    `(4,0)`

    • Similar Questions

    Explore conceptually related problems

    The tangent at P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the major axis in T and PN is the perpendicular to the x -axis, C being centre then CN.CT

    Any tangent to the ellipse is cut by the tangents at the ends of the major axis in T and T'. Then the circle whose diameter is TT' will pass through the foci.

    Equation of tangent to the ellipse (x^(2))/(9)+(y^(2))/(4) = 1 which cut-off equal intercepts on the axis, is

    Prove that if any tangent to the ellipse is cut by the tangents at the endpoints of the major axis at TandT ' ,then the circle whose diameter is T will pass through the foci of the ellipse.

    The tangent at any point on the ellipse 16x^(2) + 25^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

    Home
    Profile