The order and degree of the differential equation of the family of ellipse having the same foci are respectively (axis being coordinate axis):
Answer & explanation
Correct answer: option 4
Equation of family of ellipse is $\frac{x^2}{a^2+λ}+\frac{y^2}{b^2+λ}=1$
Foci (± ae, 0) ≡ $(±\sqrt{a^2-b^2},0)$ are same for all ellipse differentiate w. r. t. x
$\frac{x^2}{a^2+λ}+\frac{yp}{b^2+λ}=0⇒λ=\frac{-b^2x-a^2yp}{x+yp}$
∴ The D.E. is $\frac{x^2}{a^2+\frac{-b^2x-a^2yp}{x+yp}}+\frac{y^2}{b^2+\frac{-b^2x-a^2yp}{x+yp}}=1$
Hence order =1 degree 2.