Question

The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.

Options

• x² + y² + x - 2y + c = 0

• x² + y² - 2x + 4y + c = 0

• x² + y² - x + 2y + c = 0

• x² + y² + 2x - 4y + c = 0

Answer 1

The general solution of the differential equation of all circles having centre at A(- 1, 2) is x² + y² + 2x - 4y + c = 0.

Explanation:

General equation of a circle with centre (- g, - f) is

x² + y² + 2gx + 2fy + c = 0

If (- g, - f) = A (- 1, 2)

Then equation of circle,

x² + y² + 2x - 4y + c = 0