The line l is tangent to the circle with equation x^2 + y^2=10 at the point P. Determine the equation of line l.

Given:

The equation of a circle is

A tangent line l to the circle touches the circle at point P(1,3).

To find:

The equation 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(1,3). 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.

The slope of line l is and it passs through the point P(1,3). So, the equation of line l is

Adding 3 on both sides, we get

Therefore, the equation of line l is .

step-by-step explanation: