# Is the normal line perpendicular to the curve?

## How do you find the normal line to a curve?

How to Find a Normal Line to a Curve

• Take a general point, (x, y), on the parabola. and substitute.
• Take the derivative of the parabola.
• Using the slope formula, set the slope of each normal line from (3, 15) to. equal to the opposite reciprocal of the derivative at.
• Plug each of the x-coordinates (8, 4, and 12) into.

## Is the normal line perpendicular to the curve?

In geometry, a normal is an object such as a line, ray, or vector that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the (infinite) line perpendicular to the tangent line to the curve at the point.

## How do you find the normal line of a curve?

How to Find a Normal Line to a Curve

• Take a general point, (x, y), on the parabola. and substitute.
• Take the derivative of the parabola.
• Using the slope formula, set the slope of each normal line from (3, 15) to. equal to the opposite reciprocal of the derivative at.
• Plug each of the x-coordinates (8, 4, and 12) into.

Tangent

## Is the normal perpendicular to the curve?

The normal is a line at right angles to the tangent. If we have a curve such as that shown in Figure 2, we can choose a point and draw in the tangent to the curve at that point. The normal is then at right angles to the curve so it is also at right angles (perpendicular) to the tangent.

## Is the normal line always perpendicular?

The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency. Because the slopes of perpendicular lines (neither of which is vertical) are negative reciprocals of one another, the slope of the normal line to the graph of f(x) is u22121/ fu2032(x).

## What is a normal line to a curve?

The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent. A person might remember from analytic geometry that the slope of any line perpendicular to a line with slope m is the negative reciprocal u22121/m.

## How do you find the perpendicular line of a curve?

Answer: The line perpendicular to the curve at (2,1) will have slope equal to the negative reciprocal of the slope of the tangent line. Therefore, we should first determine the slope of the tangent line, which is given by the derivative of the function at the point. For any x, y (x)3×2 – 4.