CPM Homework Help : PC Problem 9-73

Find the equation of the line tangent to the circle $x^{2} + y^{2} = 25$ at the point $\left(3, 4\right)$ .

Step 1:

The radius is perpendicular to the tangent line. Use the diagram at right to determine the slope of the radius and then the slope of the tangent line.

Step 2:

Use the given point and the slope of the tangent line to write the equation.

Circle centered at the origin, passing through the points (4, comma 0), (0, comma 4), (negative 4, comma 0), & (0, comma negative 4), with red radius to labeled point (3, comma 4), & dashed line, tangent to the circle @ the point, (3, comma 4).