Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Form the differential equation from the following primitive where constants are arbitrary:
xy = a²

Form the differential equation from the following primitive where constants are arbitrary:
y = ax² + bx + c

Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x + a)² + y² = a²

Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)² − y² = a²

Form the differential equation of the family of curves represented by the equation (a being the parameter):
 (x − a)² + 2y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x² + y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x² − y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y² = 4ax

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x² + (y − b)² = 1

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
(x − a)² − y² = 1

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y² = 4a (x − b)

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x² + y² = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = e^ax