The line l is tangent to the circle with equation x² + y2 = 169 at the point P. By thinking about the radius or otherwise, determine the gradient of the line l.

Given:

The equation of a circle is

A tangent line l to the circle touches the circle at point P(12,5).

To find:

The gradient of the line l.

Solution:

Slope formula: If a line passes through two points, then the slope of the line is

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is

We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

Therefore, the gradient or slope of the tangent line l is .

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation: