Tangents and Normals A tangent is the line that touches a circle at one point, with the circle centred at the origin. The slope of the tangent at a give...
A tangent is the line that touches a circle at one point, with the circle centred at the origin.
The slope of the tangent at a given point is called the tangent slope. Tangent slopes can be positive, negative, or zero, depending on the relationship between the radius of the circle and the distance from the origin to the point of tangency.
The normal is the line that is perpendicular to the tangent. It is drawn from the same point as the tangent, at a right angle to it.
The slope of the normal is the negative reciprocal of the slope of the tangent. This means that the slopes of the tangent and normal are negative reciprocals of each other.
Here's a concrete example to illustrate the concepts:
Imagine a circle centred at the origin.
Draw the tangent at a specific point on the circle.
Draw the normal to the tangent at that point.
Measure the slopes of the tangent and normal.
Observe that the slopes are negative reciprocals of each other.
By understanding the concepts of tangents and normals, we can find the equations of circles, lines, and other shapes