Telangana Board Solutions for Exercise 1: Exercise 8(a)

Obtain the differential equation which corresponds to the ellipses with centers at the origin and having coordinate axes as axes.

Form the differential equation the family of curves $y=a{e}^{3x}+b{e}^{4x}$ where $a$ and $b$ are the parameters.

Form the differential equation of the following family of curves where parameters are given in bracket: $y=a{x}^2+bx$; $(a,b)$

Form the differential equation of the following family of curves where parameters are given in bracket: $a{x}^2+b{y}^2=1$; $(a,b)$

Form the differential equation of the following family of curves where parameters are given in bracket: $xy=a{x}^2+b/x$; $(a,b)$

Obtain the differential equation which corresponds to the family of circles which touch the $Y$-axis at the origin

Obtain the differential equation which corresponds to the parabolas each of which has a latus rectum $4a$ and whose axes are parallel to $X$-axis

Obtain the differential equation which corresponds to the parabolas having their foci at the origin and axis along the $X$-axis.