The parametric point on the circle `x^(2)+y^(2)=a^(2)` is :

Options

A. `(acostheta,asintheta)`
B. `(acostheta, bsintheta)`
C. `(bcostheta, asintheta)`
D. None of these

Answer

To find the parametric point on the circle defined by the equation \(x^2 + y^2 = a^2\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation of the Circle**:
The given equation is \(x^2 + y^2 = a^2\). This is the standard form of a circle centered at the origin \((0, 0)\) with radius \(a\).

**Hint**: Recognize that the general form of a circle's equation is \(x^2 + y^2 = r^2\), where \(r\) is the radius.

2. **Compare with the Standard Form**:
From the equation \(x^2 + y^2 = a^2\), we can see that the radius \(r\) is equal to \(a\).

**Hint**: Identify the radius by comparing the given equation with the standard circle equation.

3. **Use Parametric Equations**:
The parametric equations for a circle of radius \(r\) are given by:
\[ x = r \cos \theta \]
\[ y = r \sin \theta \]
Since we have determined that \(r = a\), we can substitute \(a\) into these equations.

**Hint**: Remember that the parametric equations for circles involve trigonometric functions.

4. **Substitute the Radius**:
Substitute \(r = a\) into the parametric equations:
\[ x = a \cos \theta \]
\[ y = a \sin \theta \]

**Hint**: Ensure that you replace \(r\) with the correct value from the previous step.

5. **Write the Parametric Point**:
The parametric point on the circle can now be expressed as:
\[ (x, y) = (a \cos \theta, a \sin \theta) \]

**Hint**: Combine the results from the previous step to form the final parametric point.

### Final Answer:
The parametric point on the circle \(x^2 + y^2 = a^2\) is given by:
\[ (a \cos \theta, a \sin \theta) \]