1.

If `sqrt(1-x^(2))+sqrt(1-y^(2))=a`, then what is `(dy)/(dx)` equal to?A. `sqrt((1-x^(2))(1-y^(2)))`B. `sqrt((1-y^(2))/(1-x^(2)))`C. `sqrt((1-x^(2))/(1-y^(2)))`D. None of these

Answer» Correct Answer - D
Let `sqrt(1-x^(2))+sqrt(1-y6(2))=a`
On differentiating w.r.t. x, we get
`(1)/(2sqrt(1-x^(2)))(-2x)+(1(-2y))/(2sqrt(1-y^(2)))(dy)/(dx)=0`
`rArr (-x)/(sqrt(1-x^(2)))-(y)/(sqrt(1-y6(2)))(dy)/(dx)=0`
`rArr (-x)/(sqrt(1-x^(2)))=(y)/(sqrt(1-y^(2)))(dy)/(dx)`
`rArr (dy)/(dx)=-(x)/(y)sqrt((1-y^(2))/(1-x^(2)))`


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