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Eliminate theta from the following equat...

Eliminate `theta` from the following equation : `x cos theta - y sin theta = a, x sin theta + y cos theta = b`

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Knowledge Check

  • The method of eliminating 'theta' from two given equations involving trigonometrical functions of 'theta' . By using given equations involving 'theta' and trigonometrical identities, we shall obtain an equation not involving 'theta' . On the basis of above information answer the following questions. After eliminating 'theta' from equations (x cos theta)/(a) + (y sin theta)/(b)=1 and x sin theta-y cos theta= sqrt((a^(2)sin^(2) theta+ b^(2) cos^(2) theta)) , we get

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

  • The eliminant of theta from x cos theta - y sin theta = 2 , x sin theta + y cos theta = 4 will give

    A
    `x^2 + y^2 = 20`
    B
    `3x^2 + y^2 = 20`
    C
    `x^2 - y^2 = 20`
    D
    `x^2-y^2 =20`

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