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The differential equation whose solution...

The differential equation whose solution is
` (x - alpha)^(2) + (y - beta)^(2) = a^(2) ` [ for all ` alpha " and " beta` where a is constant ] of is -

A

order 2

B

order 3

C

degree 2

D

degree 3

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Prove that , (x - alpha )^(2) + (y - beta)^(2) = a^(2) . for all alpha " and " beta satisfiles the differential equation (1 + y_(1)^(2))^(3) = (ay_(2))^(2) .

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Knowledge Check

  • If the axes are transferred to parallel axes through the point (alpha ,- beta), then the equation of the circle (x- alpha)^(2) +(y - beta )^(2) =a^(2) reduces to the form-

    A
    `x^(2)+y^(2) =a^(2)`
    B
    `x ^(2) +(y+beta )^(2) =a^(2)`
    C
    `x^(2) + (y+2 beta)^(2) =a^(2)`
    D
    `x ^(2) + (y- 2 beta )^(2) =a^(2)`

  • If sin(3alpha-beta)=1 and cos(2alpha+beta)=1/2 , then the values of alpha and beta will be respectively :

    A
    `60^@, 30^@`
    B
    `30^@, 0^@`
    C
    `60^@, 0^@`
    D
    `30^@, 45^@`

  • If alpha + beta =(pi)/(2)and beta + gamma =alpha, then the value of tan alpha is -

    A
    `tan beta +tan gamma`
    B
    `2 tan beta + tan gamma`
    C
    `tan beta + 2 tan gamma`
    D
    `2(tan beta+ tan gamma)`

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    If the axis are transferred to parallel axis throught the point (alpha,beta) , then equation of the circle (x-alpha)^(2)+(y-beta)^(2)=a^(2) reduces to the form-

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