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On the ellipse 4x^(2)+9y^(2)=1, the poin...

On the ellipse `4x^(2)+9y^(2)=1`, the points at which the tangent are parallel to the line `8x=9y` are

A

(2/5,1/5)

B

(-2/5, 1/5)

C

(-2/5 , -1/5)

D

none of these

Text Solution

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The correct Answer is:
B
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On the ellipse 4x^(2)+9y^(2)=1, the points at which the tangents are parallel to the line 8x=9y are ((2)/(5),(1)/(5))( b ) (-(2)/(5),(1)/(5))(-(2)/(5),-(1)/(5))( d) ((2)/(5),-(1)/(5))

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Knowledge Check

  • On the ellipse 4x^2 +9y^2 = 1 , the points at which the tangents are parallel to the line 8x = 9y are

    A
    `(2/5, 1/5)`
    B
    `(-2/5, 1/5)`
    C
    `(- 2/5, -1,5)`
    D
    `(2/5, -1/5)`

  • On the ellipse x^2/4+y^2/9=1 , one of the points at which the normal are parallel to the line 2x-y=1 is

    A
    `(2/(sqrt(10)), 9/(sqrt(10)))`
    B
    `(2/(sqrt(10)), (-9)/(sqrt(10)))`
    C
    `((-2)/(sqrt(10)), 9/(sqrt(10)))`
    D
    None of these

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