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Express the polar equation r-2costheta i...

Express the polar equation `r-2costheta` in rectangular coordinates.

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We use the formulas `r^2=x^2+y^2` and `x=rcostheta`. ltbr Given `r=2costheta`. Therefore,
`r^2=2rcostheta`
or `x^2+y^2=2x`
or `x^2x+y^2=0`
or `x^2-2x+1+y^2=1`
or `(x-1)^2+y^2=1`.
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Knowledge Check

  • The solution of the equation |(costheta,sintheta,costheta),(-sintheta,costheta,sintheta),(-costheta, -sintheta,costheta)|=0 is -

    A
    `(2n+1)(pi)/(2)`
    B
    `n pi `
    C
    `n pi +(-1)^(n) (pi)/(4)`
    D
    `1n pi pm (pi)/(4)`

  • ABCD is a rectangular A circle circumscribing the rectangle. The coordinates of A and C are (-3, 4) and (5, 4) respectively. Equation of circle will be -

    A
    `x^(2) + y^(2) - 2x - 4y - 15 = 0`
    B
    `x^(2) + y^(2) + 2x - 4y - 16 = 0`
    C
    `x^(2) + y^(2) + 2x + 4y - 4 = 0`
    D
    None of these

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