The co-ordinates of a point on the parabola `y^(2)=8x` whose ordinate is twice of abscissa, is :

Options

A. (2,4)
B. (-2,4)
C. (-2,-4)
D. None of these.

Answer

To find the coordinates of a point on the parabola \( y^2 = 8x \) where the ordinate (y-coordinate) is twice the abscissa (x-coordinate), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parabola Equation**:
The given equation of the parabola is:
\[ y^2 = 8x \]

2. **Express the Relationship Between Coordinates**:
We know that the ordinate (y-coordinate) is twice the abscissa (x-coordinate). Thus, we can express this as:
\[ y = 2x \]

3. **Substitute y in the Parabola Equation**:
Substitute \( y = 2x \) into the parabola's equation:
\[ (2x)^2 = 8x \]
Simplifying this gives:
\[ 4x^2 = 8x \]

4. **Rearrange the Equation**:
Rearranging the equation leads to:
\[ 4x^2 - 8x = 0 \]

5. **Factor the Equation**:
Factor out the common term:
\[ 4x(x - 2) = 0 \]

6. **Solve for x**:
Setting each factor to zero gives:
\[ 4x = 0 \quad \Rightarrow \quad x = 0 \]
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]

7. **Find Corresponding y Values**:
Now, we find the corresponding y-values for both x-values using \( y = 2x \):
- For \( x = 0 \):
\[ y = 2(0) = 0 \quad \Rightarrow \quad (0, 0) \]
- For \( x = 2 \):
\[ y = 2(2) = 4 \quad \Rightarrow \quad (2, 4) \]

8. **Conclusion**:
The coordinates of the points on the parabola are \( (0, 0) \) and \( (2, 4) \). Since we are looking for a point where the ordinate is twice the abscissa, we can select:
\[ (2, 4) \]

### Final Answer:
The coordinates of the point on the parabola \( y^2 = 8x \) whose ordinate is twice the abscissa are \( (2, 4) \).