If abscissa of orthocentre of a triangle inscribed in a rectangular hyperbola `xy=4` is `(1)/(2)`, then the ordinate of orthocentre of triangle is

Answer

To find the ordinate of the orthocenter of a triangle inscribed in the rectangular hyperbola \(xy = 4\), given that the abscissa (x-coordinate) is \(\frac{1}{2}\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that the orthocenter of the triangle has an abscissa (x-coordinate) of \(\frac{1}{2}\). We denote the coordinates of the orthocenter as \((x_1, y_1)\), where \(x_1 = \frac{1}{2}\).

2. **Use the Equation of the Hyperbola**:
The orthocenter lies on the hyperbola defined by the equation \(xy = 4\). Therefore, the coordinates of the orthocenter must satisfy this equation.

3. **Substitute the Abscissa into the Hyperbola Equation**:
Substitute \(x_1\) into the hyperbola equation:
\[ x_1 \cdot y_1 = 4 \]
Substituting \(x_1 = \frac{1}{2}\):
\[ \frac{1}{2} \cdot y_1 = 4 \]

4. **Solve for the Ordinate \(y_1\)**:
To find \(y_1\), multiply both sides of the equation by 2:
\[ y_1 = 4 \cdot 2 = 8 \]

5. **Conclusion**:
The ordinate of the orthocenter of the triangle is \(y_1 = 8\).

### Final Answer:
The ordinate of the orthocenter of the triangle is \(8\).