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The problem asks for the equation of the tangent line to the circle \( x^2 + y^2 = 49 \) that passes through the point \((-2, 3)\).

1. **Find the slope of the tangent line:**
   The slope of the tangent line to the circle at any point \((x_1, y_1)\) is given by:
   \[
   m = -\frac{x_1}{y_1}
   \]
   We will first use this formula.

2. **Find the equation of the tangent line:**
   The equation of the tangent line at point \((x_1, y_1)\) on the circle \(x^2 + y^2 = r^2\) is:
   \[
   x_1x + y_1y = r^2
   \]
   Here, \( r^2 = 49 \).

3. **Verify which option passes through \((-2, 3)\):**
   After finding the tangent line, we check which one of the provided options is correct.

Let's go through the calculations.The equation of the tangent line to the circle \( x^2 + y^2 = 49 \) that goes through the point \((-2, 3)\) is:

\[
-2x + 3y = 49
\]

However, none of the provided options passes through the point \((-2, 3)\). It seems there may be an error in the given options or there might be a different interpretation of the problem. 

Would you like to further analyze this issue or have more details? Here are some related questions to consider:

1. What are the other methods to find the equation of a tangent line to a circle?
2. How do you find the slope of a tangent to a circle geometrically?
3. What is the general form of a tangent to a circle given in parametric coordinates?
4. How can you verify whether a line is tangent to a circle?
5. How does the perpendicular slope relate to the radius of a circle?

**Tip:** Always verify your solution by substituting the point into the final equation.

Persamaan garis singgung lingkaran x^2 + y^2 = 49 yang melalui titik (-2, 3) adalah...

Solve for the equation of the tangent line to the circle x^2 + y^2 = 49 passing through the point (-2, 3). This geometry problem includes key concepts like tangent lines, circle equations, and slope calculations. Suitable for Grades 10-12 students.

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