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

### Step 1: General Form of a Tangent Line to a Circle
For a circle with the equation \(x^2 + y^2 = r^2\), the equation of the tangent line at a point \((x_1, y_1)\) outside the circle is given by:

\[
x_1 x + y_1 y = r^2
\]

In this case, the circle equation is \(x^2 + y^2 = 49\), meaning \(r^2 = 49\).

### Step 2: Applying the Point \((-2, 3)\)
Using the point \((-2, 3)\), we substitute \(x_1 = -2\) and \(y_1 = 3\) into the general formula for the tangent line:

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

This is the equation of the tangent line.

### Step 3: Checking the Answer Options
The correct answer is the option that matches the equation \(-2x + 3y = 49\). Therefore, the correct choice is **option c**.

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### 5 Related Questions:
1. What is the general equation of a circle in Cartesian coordinates?
2. How do you derive the equation of a tangent to a circle?
3. Can a circle have more than one tangent line through a given point outside the circle?
4. How would you find the point of tangency between the line and the circle?
5. What are some applications of tangent lines in geometry and physics?

### Tip:
For any circle with center at the origin, the tangent at a point can be quickly found by multiplying the coordinates of the point by \(x\) and \(y\) respectively and setting the result equal to the square of the radius.

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

Learn how to find the equation of the tangent line to the circle x^2 + y^2 = 49 passing through the point (-2, 3). This problem covers key geometric concepts, including the equation of a tangent line to a circle. Suitable for high school students.

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