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If p is the length of the perpendicular ...

If p is the length of the perpendicular from a focus upon the tangent at any point P of the the ellipse `x^2/a^2+y^2/b^2=1` and r is the distance of P from the foicus , then `(2a)/r-(b^2)/(p^2)` is equal to

A

`-1`

B

0

C

1

D

2

Text Solution

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The correct Answer is:
C
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If p is the length of the perpendicular from a focus upon the tangent at any point P of the the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and rs the distance of P from the foicus,then (2a)/(r)-(b^(2))/(p^(2)) is equal to

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Knowledge Check

  • The locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 , is

    A
    `(x^2+y^2)^2=ax^2+by^2`
    B
    `(x^2+y^2)=a^2x^2+b^2y^2`
    C
    `(x^2+y^2)^2=a^2x^2+b^2y^2`
    D
    None of the above
  • The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

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    `x^(2) + y^(2) = b^(2)`
    B
    `x^(2) + y^(2) = a^(2)`
    C
    `x^(2) + y^(2) = a^(2) + b^(2)`
    D
    none of these
  • If P is the length of perpendicluar drawn from the origin to any normal to the ellipse x^(2)/25+y^(2)/16=1 , then the maximum value of p is

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