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Find the locus of the point (x,y) where ...

Find the locus of the point (x,y) where
`x=a+bcostheta,y=b+asintheta`

Text Solution

Verified by Experts

The correct Answer is:
`((x-a)^(2))/(b^(2))+((y-b)^(2))/(a^(2))=1`
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Knowledge Check

  • The locus of the point represented by x=cos^(2)t,y=2sint is

    A
    `y^(2)=4x`
    B
    `y^(2)=4x+1`
    C
    `y^(2)+4x=1`
    D
    `y^(2)+4x=4`

  • The locus of the centroid of the triangle with vertices at (acostheta,asintheta) , (bsintheta-bcostheta) and (1,0) is (here, theta is a parameter)

    A
    `(3x+1)^(2)+9y^(2)=a^(2)+b^(2)`
    B
    `(3x-1)^(2)+9y^(2)=a^(2)-b^(2)`
    C
    `(3x-1)^(2)+9y^(2)=a^(2)+b^(2)`
    D
    `(3x+1)^(2)+9y^(2)=a^(2)-b^(2)`

  • The locus of the centroid of the triangle with vertices at (acostheta,asintheta),(bsintheta,-bcostheta) and (1,0) is (Here theta is a parameter)

    A
    `(3x-1)^(2)+9y^(2)=a^(2)+b^(2)`
    B
    `(3x+1)^(2)+9y^(2)=a^(2)+b^(2)`
    C
    `(3x+1)+9y^(2)=a^(2)+b^(2)`
    D
    `(3x-1)^(2)+9y^(2)=a^(2)-b^(2)`

    • Similar Questions

    Explore conceptually related problems

    Find the Cartesian equation of the locus whose parametric equations are x=acostheta,y=asintheta where theta is the parameter.

    Find the slope of the normal to the curve x=1-asintheta, y=bcos^(2)theta at theta=(pi)/(2)

    Find the locus of the point which represented by x = t^(2) +t +1, y = t^(2) - t +1

    Find the locus of the point of intersection of tangents to the ellipse x^2/a^2+y^2/b^2=1 at the points the sum of whose ordinates are constant.

    The locus of the point of intersection of the lines x cos theta+y sin theat=a, x sin theta-y cos theta=b where 0 le theta lt 2pi is a circle of radius

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