Q18 of 462 Page 22

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

Equation of required hyperbola is

Where a,b are arbitrary constants

Differentiating with respect to x we get,

Again, differentiating with respect to x we get,

Substituting this value of in (ii) we get,

The required differential equation is

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

y = e^ax

Form the differential equation representing the family of ellipses having the center at the origin and foci on the x - axis.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.