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If the chords of contact of tangents from two poinst `(x_1, y_1)` and `(x_2, y_2)` to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` are at right angles, then find the value of `(x_1x_2)/(y_1y_2)dot`

A

`a^(4)/b^(4)`

B

`b^(4)/a^(4)`

C

`-a^(4)/b^(4)`

D

`-b^(4)/a^(4)`

Text Solution

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The correct Answer is:
C
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If the chords of contact of tangents from two poinst (x_(1),y_(1)) and (x_(2),y_(2)) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 are at right angles,then find the value of (x_(1)x_(2))/(y_(1)y_(2))

If the chords of contact of tangents fromtwo points (x_(1),y_(1)) and (x_(2),y_(2)) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angles,then (x_(1)x_(2))/(y_(1)y_(2)) is equal to (a) (a^(2))/(-b^(2))( b) (b^(2))/(-a^(2))( c) (b^(4))/(-a^(4))

Knowledge Check

  • If chords of contact of the tangent from two points (x_1,y_1) and (x_2,y_2) to the ellipse x^2/a^2+y^2/b^2=1 are at right angles , then (x_1x_2)/(y_1y_2) is equal to

    A
    `a^2/b^2`
    B
    `(-b^2)/a^2`
    C
    `(-a^4)/b^4`
    D
    `b^4/a^4`

  • If the chords of contact of tangents from two points (x_(1),y_(1)) and (x_(2),y_(2)) to the ellipse (x^(2))/(5^(2))+(y^(2))/(6)^(2) =1 are at right angles then (x^(1),x_(2))/(y_(1)y_(2)) is equal to

    A
    `-(5/6)^(4)`
    B
    `(6/5)^(4)`
    C
    `-(6/5)^(4)`
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    `(5/6)^(4)`

  • If the chords of contact of tangents from two points (x_(1), y_(1)) and (x_(2), y_(2)) to the angles, then (x^(1)x_(2))/(y_(1)y_(2)) is equal to

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    B
    `-(b^(2))/(a^(2))`
    C
    `-(a^(4))/(b^(4))`
    D
    `(b^(4))/(a^(4))`

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