Find the equation of a circle which touches y-axis at a distance of 4units from the origin and cuts an intercept of 6units along the positive direction of x-a xis

Explanation

To find the equation of the circle that touches the y-axis at a distance of 4 units from the origin and cuts an intercept of 6 units along the positive direction of the x-axis, we can follow these steps:

### Step 1: Identify the center of the circle
Since the circle touches the y-axis at a distance of 4 units from the origin, the center of the circle must be at (4, k) where k is the y-coordinate of the center. The distance of the center from the y-axis is equal to the radius of the circle.

### Step 2: Determine the radius
The circle cuts an intercept of 6 units along the positive direction of the x-axis. This means that the circle intersects the x-axis at two points: one at (0, 0) and another at (6, 0). The radius of the circle can be determined by the distance from the center (4, k) to the x-axis.

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