Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.`y^2=a(b^2-x^2)`

Explanation

Given, `y^(2)=a(b^(2)-x^(2))`……`(1)`
`implies2yy'=a(0-2x)implies2yy'=a(-2x)`
`implies yy'=-ax`…………..`(2)`
`impliesyy'+(-y)^(2=-a`………..`(3)`
Now, pu the value of a from equation `(3)` to equation `(2)` ,
`yy'=[yy'+(-y)^(2)]ximpliesyy'=x[(-y)^(2)+yy']`
which is the required differential equation.