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When the coordinate axes are rotated by ...

When the coordinate axes are rotated by an angle `tan^(-1) ((3)/(4))` about the origin, then the equation `x^(2) + y^(2) =9` is transformed to the equation.

A

`x^(2) -y^(2) =9`

B

`x^(2) + y^(2) + 2xy = 4`

C

`x^(2) + y^(2)= 9`

D

`x^(2) - y^(2) + 9 = 0`

Text Solution

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The correct Answer is:
C
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When the axes are rotated through an angle (pi)/(4) , find the transformed equation of 3x^2 + 10xy + 3y^2 = 9 .

When the axes are rotated through an angle (pi)/(6) find the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) .

Knowledge Check

  • If the coordinate axes are rotated through an angle (pi)/(6) about the origin, then transformed equation of sqrt(3)x^2-4xy+sqrt(3)y^2=0 is

    A
    `sqrt(3)y^2+xy=0`
    B
    `x^2-y^2=0`
    C
    `sqrt(3)y^2-xy=0`
    D
    `sqrt(3)y^2-2xy=0`

  • If the corrdinate axes are rotated through an angle (pi)/(6) about the origin, then the transformed equation of sqrt(3)x^(2) - 4xy + sqrt(3)y^(2) = 0 is

    A
    `sqrt(3)y^(2) + xy = 0`
    B
    `x^(2) - y^(2) = 0`
    C
    `sqrt(3)y^(2) - xy = 0`
    D
    `sqrt(3) y^(2) - 2xy = 0`

  • If the axes are rotated through an angle 30^(0) about the origin then the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) is

    A
    `X^(2) +Y^(2) = a^(2)`
    B
    `X^(2)-Y^(2)=a^(2)`
    C
    `X^(2)+Y^(2)=2a^(2)`
    D
    `X^(2)-Y^(2)=2a^(2)`

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