Question

find the differential equation of all conics whose centre lies at origin​

Answer 1

Given:

The differential equation of all conics whose centre lies at origin​

To find:

Find the differential equation of all conics whose centre lies at origin​

Solution:

From given, we have,

The general equation of all conics with center at origin can be written as

ax² + 2hxy + by² + c = 0

Divide the above equation by 'a', we get

x² + (2h/a) xy + (b/a) y² + (c/a) = 0

As it has three arbitrary constants, thus, the differential equation is of order 3.

Therefore the differential equation of all conics whose centre lies at the origin​ is x² + (2h/a) xy + (b/a) y² + (c/a) = 0