Question

The equation of the circle with centre on the x axis and passing through the origin is: 

(a) x² – 2ax + y² = 0 

(b) y² – 2ay + x² = 0 

(c) x² + y² = a² 

(d) x² – 2ay + y² = 0

Answer 1

(a) x² – 2ax + y² = 0

Let the centre on the x-axis as (a, 0). 

This circle passing through the origin so the radius

Now centre (h, k) = (a, 0) 

Radius = a 

Equation of the circle is (x – a)² + (y – 0)² = a²

⇒ x² – 2ax + a² + y² = a² 

⇒ x² – 2ax + y² = 0