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

NCERT Solutions for Class 12 Maths Chapter 9 - Image 45

NCERT Solutions for Class 12 Maths Chapter 9 - Image 46

NCERT Solutions for Class 12 Maths Chapter 9 - Image 47

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

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

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

\end{array}\]

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