Question

Find the equation of a circle with a radius of 4 units and touch both the co-ordinate axes having centre in the third quadrant. 

Answer 1

The radius of the circle = 4 units 

Since the circle touches both the co-ordinate axes and its centre is in the third quadrant, the centre of the circle is C(-4, -4).

The equation of a circle with centre at (h, k) and radius r is given by (x – h)² + (y – k)² = r² 

Here, h = -4, k = -4, r = 4

the required equation of the circle is 

⇒ [x – (-4)]² + [y – (-4)]² = 4² 

⇒ (x + 4)² + (y + 4)² = 16 

⇒ x² + 8x + 16 + y² + 8y + 16 – 16 = 0 

⇒ x² + y² + 8x + 8y + 16 = 0