Question

Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.

Answer 1

Let the co-ordinates of the centre of the required circle be C(h, 0).

Since the circle passes through the origin i.e., O(0,0),

OC = radius

∴ `sqrt(("h" - 0)^2 + (0 - 0)^2` = 4

∴ h² = 16

∴ h = ± 4

∴ the co-ordinates of the centre are (4, 0) or (– 4, 0).

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 = 0, r = 4

∴ The required equation of the circle is

(x – 4)² + (y – 0)² = 4² or (x + 4)² + (y – 0)² = 4²

∴ x² – 8x + 16 + y² = 16 or x² + 8x + 16 + y² = 16

∴ x² + y² – 8x = 0 or x² + y² + 8x = 0