Find the equation of locus of the point which is at a distance 5 unit from the Y-axis.

Answer

To find the equation of the locus of a point that is at a distance of 5 units from the Y-axis, we can follow these steps:

### Step 1: Understand the position of the point
A point that is at a distance of 5 units from the Y-axis can be located either to the right or to the left of the Y-axis.

### Step 2: Determine the possible x-coordinates
Since the distance from the Y-axis is measured along the x-direction, the x-coordinates of the points can be either +5 or -5. Therefore, the possible x-coordinates are:
- x = 5 (5 units to the right of the Y-axis)
- x = -5 (5 units to the left of the Y-axis)

### Step 3: Write the equations for the locus
The two lines that represent the locus of the points are:
1. x = 5
2. x = -5

### Step 4: Combine the equations
We can combine these two equations into a single equation. The absolute value notation can be used to express this:
- |x| = 5

### Step 5: Convert to standard form
We can also express this equation in another form by squaring both sides:
- (|x|)^2 = 5^2
- x^2 = 25

### Final Answer
Thus, the equation of the locus of the point which is at a distance of 5 units from the Y-axis can be expressed as:
1. |x| = 5
2. x^2 = 25