Form the differential equation of the family of hyperbola having foci on x-axis and center at the origin.

Explanation

Equation of hyperbola is given by `(x^2)/(a^2)-(y^2)/(b^2)=1 `


Differentiating both the sides, we get


`frac{2x}{a^{2}}-frac{2yy’}{b^{2}}=0`` \ \ \ \ …(1)`


Again differentiating w.r.t `x`, we get


`frac{1}{a^{2}}- (frac{1}{b^{2}}) [(y)^{2}+y y'’]`


`frac{1}{a^{2}}= (frac{1}{b^{2}}) [(y)^{2}+y y'’ ]`


Putting this in equation `(1)`, we get


` (frac{x}{b^{2}}) [(y’)^{2}+y y’’]-frac{y y’}{b^{2}}=0`


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