If a an arbitrary constant, then solution of the differential equation `(dy)/(dx)+sqrt((1-y^(2))/(1-x^(2)))=0` is

Options

A. `xsqrt(1-y^(2))+ysqrt(1-x^(2))=a`
B. `ysqrt(1-y^(2))+xsqrt(1-x^(2))=a`
C. `xsqrt(1-y^(2))-ysqrt(1-x^(2))=a`
D. `ysqrt(1-y^(2))-xsqrt(1-x^(2))=a`

Answer

A

Explanation

We have,
`(dy)/(dx)+sqrt((1-y^(2))/(1-x^(2)))=0`
`rArr" "sqrt(1-x^(2))dy+sqrt(1-y^(2))dx=0`
`rArr" "(1)/(sqrt(1-x)^(2))dx+(1)/(sqrt(1-y^(2)))dy=0`
`rArr" "sin^(-1)x+sin^(-1)y=sin^(-1)a" [On integrating]"`
`rArr" "sin^(-1)(xsqrt(1-y^(2))+ysqrt(1-x^(2)))=sin^(-1)a`
`rArr" "xsqrt(1-y^(2))+ysqrt(1-x^(2))-a`