India Site

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.

NCERT Solutions for Class 12 Maths Chapter 9 - Image 41

\[\begin{array}{*{35}{l}}

\Rightarrow ~-x\text{ }{{\left( y’ \right)}^{2}}~-\text{ }xyy”\text{ }+\text{ }yy’\text{ }=\text{ }0  \\

\Rightarrow ~xyy”\text{ }+\text{ }x\text{ }{{\left( y’ \right)}^{2}}~-\text{ }yy’\text{ }=\text{ }0  \\

\end{array}\]

Hence, xyy” + x (y’)2 – yy’ = 0 is the required differential equation.