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The number of normals to the hyperbola (...

The number of normals to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` from an external point, is

A

`2`

B

`4`

C

`6`

D

`3`

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Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

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Knowledge Check

  • The line lx+my=n is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 if

    A
    `(a^(2))/(l^(2))+(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2))`
    B
    `(a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)-b^(2))^(2))/(n^(2))`
    C
    `(a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2))`
    D
    none

  • Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

    A
    `(x^(2)-+y^(2))^(2)((a^(2))/(x^(2))+(b^(2))/(y^(2))) =(a^(2)-b^(2))^(2)`
    B
    `(x^(2)+y^(2))^(2)((a^(2))/(x^(2))-(b^(2))/(y^(2)))=(a^(2)+b^(2))^(2)`
    C
    `(x^(2)+y^(2))^(2) ((x^(2))/(a^(2))-(y^(2))/(b^(2))) =(a^(2)+b^(2))^(2)`
    D
    None of these

  • Let P(6,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at the point P intersects the x-axis at (9,0) then the eccentricity of the hyperbola is

    A
    `sqrt((5)/(2))`
    B
    `sqrt((3)/(2))`
    C
    `sqrt(2)`
    D
    `sqrt(3)`

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