Equation of circle of radius 5, centred on X-axis and touch Y-axis , is

Options

A. `x^(2) + y^(2) pm 5x = 0`
B. `x^(2) + y^(2) pm 5y = 0 `
C. `x^(2) + y^(2) pm 10y = 0 `
D. `x^(2) + y^(2) pm 10x = 0 `

Answer

To find the equation of a circle with a radius of 5, centered on the X-axis, and touching the Y-axis, we can follow these steps:

### Step 1: Understand the properties of the circle
The center of the circle lies on the X-axis, which means its y-coordinate is 0. The radius is given as 5, and since the circle touches the Y-axis, the distance from the center to the Y-axis must be equal to the radius.