A curve C has the property that its intial ordinate of any tangent drawn is less the abscissa of the point of tangency by unity.
Statement I. Differential equation satisfying tha curve is linear.
Statement II. Degree of differential equation is one.

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 derive the differential equation that describes the curve \( C \) based on the given property of its tangents.

### Step-by-Step Solution:

1. **Understanding the Tangent Line**:
The equation of the tangent line at a point \((x_1, y_1)\) on the curve can be expressed as:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope of the tangent at that point, which can be represented as \( \frac{dy}{dx} \).

2. **Finding the Initial Ordinate**:
To find the initial ordinate (the y-intercept) of the tangent line, we set \( x = 0 \):
\[ y - y_1 = m(0 - x_1) \implies y = y_1 - mx_1 \]
Thus, the initial ordinate is \( y = y_1 - mx_1 \).

3. **Using the Given Property**:
According to the problem, the initial ordinate is less than the abscissa of the point of tangency by unity:
\[ y_1 - mx_1 < x_1 - 1 \]
Rearranging this inequality gives:
\[ mx_1 - y_1 < 1 - x_1 \]

4. **Substituting the Slope**:
Since \( m = \frac{dy}{dx} \), we can rewrite the inequality as:
\[ \frac{dy}{dx} x_1 - y_1 < 1 - x_1 \]

5. **Rearranging the Equation**:
Rearranging the terms leads to:
\[ \frac{dy}{dx} x_1 - y_1 + x_1 < 1 \]
This can be rewritten as:
\[ \frac{dy}{dx} x_1 - y_1 = 1 - x_1 \]

6. **Dividing by \( x_1 \)**:
Dividing the entire equation by \( x_1 \) gives:
\[ \frac{dy}{dx} - \frac{y_1}{x_1} = \frac{1 - x_1}{x_1} \]

7. **Expressing in Standard Form**:
Letting \( y = y_1 \) and \( x = x_1 \), we can express this as:
\[ \frac{dy}{dx} + \frac{y}{x} = \frac{1}{x} - 1 \]
This is a linear first-order differential equation of the form:
\[ \frac{dy}{dx} + P(x)y = Q(x) \]

8. **Conclusion**:
Since we have derived a linear differential equation, we can conclude that:
- **Statement I**: The differential equation satisfying the curve is linear (True).
- **Statement II**: The degree of the differential equation is one (True).

### Final Answer:
Both statements are true.