Home
Class 12
MATHS
tangent is drawn at point P (x1, y1) on ...

tangent is drawn at point `P (x_1, y_1)` on the hyperbola `x^2/4-y^2=1.` If pair of tangents are drawn from any point on this tangent to the circle `x^2+y^2=16` such that chords of contact are concurrent at the point `(x_2, y_2)` then

A

`x_(2)/x_(1) = 4`

B

`y_(2)/y_(1) = 16`

C

`y_(2)/y_(1) = - 16`

D

`(x_(2)/x_(1))^(2) + y_(2)/y_(1) = 0 `

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    FIITJEE|Exercise COMPREHENSIONS|9 Videos

  • HYPERBOLA

    FIITJEE|Exercise MATCH THE COLUMN|6 Videos

  • HYPERBOLA

    FIITJEE|Exercise ASSIGNMENT PROBLEMS ( OBJECTIVE) Level - I|47 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

Tangent is drawn at any point (x_1,y_1) on the parabola y^2=4ax . Now tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass throught a fixed point (x_2,y_2) Prove that 4(x_1/x_2)+(y_1/y_2)^2=0 .

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a)x_1,a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c)-4,(y_1)/(y_2),(x_1//x_2) are in GP (d) x_1x_2+y_1y_2=a^2

Knowledge Check

  • A tangent is drawn at any point (l, m), l, mne0 on the parabola y^(2)=4ax and the tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=0 (where agt0 ) such that all chords of contact pass through a fixed point (alpha,beta) , then

    A
    `alphalgt0,betamgt0`
    B
    `alphallt0,betamgt0`
    C
    `2(1/alpha)^(2)+(m/beta)^(2)=8`
    D
    `4(1/alpha)+(m/beta)^(2)=0`

  • A tangent is drawn at any point (l,m) l, m ne 0 on the parabola y ^(2) = 4 ax and the tangents are drawn from any point on this tangent to the circle x ^(2)+ y ^(2) =a ^(2) (where a gt 0) such that all chords of contact pass through a fixed point (alpha, beta), then

    A
    `alpha l gt 0, beta m lt 0`
    B
    `alpha l lt 0, beta m gt 0`
    C
    `2 ((l)/(alpha)) ^(2) +((m)/(beta))=8`
    D
    `4 ((l )/(alpha )) + ((m)/(beta))^(2) =0`

  • Pair of tangents are drawn from origin to the circle x^2 + y^2 – 8x – 4y + 16 = 0 then square of length of chord of contact is

    A
    `64/5`
    B
    `24/5`
    C
    `8/5`
    D
    `8/13`

    • Similar Questions

    Explore conceptually related problems

    If the tangents are drawn from any point on the line x+y=3 to the circle x^(2)+y^(2)+9 , then the chord of contact always passes through fixed point. Find that point

    Tangent is drawn at the point (-1,1) on the hyperbola 3x^2-4y^2+1=0 . The area bounded by the tangent and the coordinates axes is

    The chords of contact of the pair of tangents drawn from each point on the line 2x+y=4 to the circle x^2+y^2=1 pass through a fixed point

    The angle between the pair of tangents drawn from the point (2,4) to the circle x^(2)+y^(2)=4 is

    The equation of tangents drawn from the point (0,1) to the circle x^2+y^2-4x-2y+4=0 are

    Home
    Profile