Question

The center of the circle is O, and the tangent to the circle is at (7, 24) on the circle. Find an equation for line P.

Answer 1

To find the equation for line P, you need to determine the slope of the tangent line at (7, 24). The slope of the tangent line is equal to the negative reciprocal of the slope of the radius. Using the point-slope form of a line, you can write the equation of line P.

Step-by-step explanation:

To find the equation for line P, we need to determine the slope of the tangent line at (7, 24). Since the tangent line is perpendicular to the radius of the circle at the point of tangency, its slope is equal to the negative reciprocal of the slope of the radius. Assuming the radius is represented by another line passing through the center of the circle, we can use the coordinates of the center and the given point on the tangent to calculate the slope of the radius. Once we have the slope of the tangent, we can write the equation of line P using the point-slope form.

1. 
   
3. Let the coordinates of the center of the circle be (h, k).
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6. Use the formula for the slope of a line passing through two points, (7, 24) and (h, k), to calculate the slope of the radius.
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9. Take the negative reciprocal of the slope of the radius to find the slope of the tangent line.
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12. Use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope of the tangent and (x1, y1) are the coordinates of a point on the tangent (in this case, (7, 24)), to write the equation of line P.

By following these steps, you can find the equation for line P based on the given information about the center and the tangent of the circle.