The differential equation of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=C` is a. `y^(primeprime)/y^(prime)+y^(prime)/y-1/x=0` b. `y^(primeprime)/y^(prime)+y^(prime)/y+1/x=0` c. `y^(primeprime)/y^(prime)-y^(prime)/y-1/x=0` d. none of these

Explanation

`frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=C ldots . .(1)`

Differentiating

`frac{2 x}{a^{2}}+frac{2 y}{b^{2}} y^{prime}=0 `

`Rightarrow frac{y}{a^{2}}+frac{y}{b^{2}} y^{prime}=0 ldots . .(2)`

Again differentiating with respect to `x`, we get

`Rightarrow frac{1}{a^{2}}+frac{1}{b^{2}}(y^{prime})^{2}+frac{y}{b^{2}} y^{prime prime}=0 ldots . .(3)`

Multiplying throughout by `x`

`frac{x}{a^{2}}+frac{x}{b^{2}}(y^{prime})^{2}+frac{x y}{b^{2}} y^{prime prime}=0 ldots ldots(4)`

...