The number of tangents to the circle `x^(2)+y^(2)=5`, that can be drawn from (2,3) is

Options

A. 0
B. 1
C. 2
D. infinity

Answer

To find the number of tangents to the circle given by the equation \( x^2 + y^2 = 5 \) that can be drawn from the point \( (2, 3) \), we can follow these steps:

### Step 1: Rewrite the Circle's Equation
The equation of the circle is given as:
\[ x^2 + y^2 = 5 \]
We can rewrite this as:
\[ x^2 + y^2 - 5 = 0 \]
Let's denote this equation as \( S_1 \).

### Step 2: Substitute the Point into the Circle's Equation
We need to substitute the coordinates of the point \( (2, 3) \) into the equation \( S_1 \):
\[ S_1 = 2^2 + 3^2 - 5 \]

### Step 3: Calculate the Value of \( S_1 \)
Now, calculate \( S_1 \):
\[ S_1 = 4 + 9 - 5 = 8 \]

### Step 4: Analyze the Value of \( S_1 \)
Now we analyze the value of \( S_1 \):
- If \( S_1 > 0 \), there are 2 tangents.
- If \( S_1 = 0 \), there is 1 tangent.
- If \( S_1 < 0 \), there are 0 tangents.

Since \( S_1 = 8 \) which is greater than 0, we conclude that there are 2 tangents.

### Final Answer
The number of tangents to the circle from the point \( (2, 3) \) is:
\[ \text{2 tangents} \]

---