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 given by the equation \( x^2 + y^2 = a^2 \), we can follow these steps:

### Step 1: Identify the Circle's Center and Radius
The equation of the circle \( x^2 + y^2 = a^2 \) represents a circle centered at the origin (0, 0) with a radius \( r = a \).

### Step 2: Write the Parametric Equations
For a circle, the parametric equations can be expressed in terms of an angle \( \theta \):
- The x-coordinate is given by \( x = r \cos \theta \)
- The y-coordinate is given by \( y = r \sin \theta \)

### Step 3: Substitute the Radius
Since we have identified that the radius \( r \) is equal to \( a \), we substitute \( r \) in the parametric equations:
- \( x = a \cos \theta \)
- \( y = a \sin \theta \)

### Step 4: Write the Parametric Point
Thus, the parametric point on the circle can be represented as:
\[ (x, y) = (a \cos \theta, a \sin \theta) \]

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

---