Statement I The order of differential equation of all conics whose centre lies at origin is , 2.
Statement II The order of differential equation is same as number of arbitary unknowns in the given curve.

Options

A. Statement I is true ,and Statement II is the correct explanation for Statement I.
B. Statement I is true, Statement II is true and Statement II is the correct explanation for Statment I
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.

Answer

To solve the problem, we need to analyze both statements regarding the order of the differential equation of conics whose center lies at the origin.

### Step-by-Step Solution:

1. **Understanding the Equation of Conics**:
The general equation of a conic section with its center at the origin can be expressed as:
\[ ax^2 + 2hxy + by^2 = 1 \]
where \(a\), \(b\), and \(h\) are constants.

2. **Rearranging the Equation**:
We can rearrange the equation to express it in a standard form:
\[ ax^2 + 2hxy + by^2 - 1 = 0 \]
This form indicates that we have a polynomial equation in \(x\) and \(y\).

3. **Identifying the Constants**:
In the equation \(ax^2 + 2hxy + by^2 - 1 = 0\), we have three constants: \(a\), \(b\), and \(h\).

4. **Determining the Order of the Differential Equation**:
The order of a differential equation is determined by the number of arbitrary constants present in the equation. Since we have three constants (\(a\), \(b\), and \(h\)), the order of the differential equation is:
\[ \text{Order} = 3 \]

5. **Evaluating Statement I**:
Statement I claims that the order of the differential equation of all conics whose center lies at the origin is 2. However, we have determined that the order is actually 3. Thus, Statement I is **false**.

6. **Evaluating Statement II**:
Statement II states that the order of the differential equation is the same as the number of arbitrary unknowns in the given curve. Since we have three arbitrary constants, this statement is **true**.

### Conclusion:
- **Statement I** is false.
- **Statement II** is true.

### Final Answer:
- Statement I: False
- Statement II: True