Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by  x² - y² = cx

Find the equations of the tangent and the normal, to the curve 16x² + 9y² = 145 at the point (x₁, y₁), where x₁ = 2 and y₁ > 0.

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`

Form the differential equation from the following primitive where constants are arbitrary:
y² = 4ax

Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c² + c³

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