The degree of the differential equation satisfying `sqrt(1-x^2)+sqrt(1-y^2)=a(x-y)` is (a) 1 (b) 2 (c) 3 (d) none of these

Options

A. 1
B. 2
C. 3
D. None of these

Answer

A

Explanation

1) Putting `x=sinA` and `y=sinB` in the given relation, we get
`cosA+cosB=a(sinA-sinB)`
or `A-B=2cot^(-1)a`
or `sini^(-1)x-sin^(-1)y=2cot^(-1)a`
Differentiating w.r.t. x, we get
`1/sqrt(1-x^(2))-1/sqrt(1-y^(2))(dy)/(dx)=0`
Clearly, it is differential equation of degree one.