# How do you find the equation of a tangent to a curve?

## How do you find the equation of a tangent to a curve?

In order to find the equation of a tangent, we:

1. Differentiate the equation of the curve.
2. Substitute the value into the differentiated equation to find the gradient.
3. Substitute the value into the original equation of the curve to find the y-coordinate.

## What is the equation of a tangent?

A tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c .

What is the tangent to a curve?

tangent, in geometry, the tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point. It may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve as the second point approaches the first.

### What is the equation of tangent to the curve at P?

If y = f(x), then the slope of the curve at point a is given by y’ = f'(x = a) = tan θ = m. Calculation: Given: curve y = memx where m > 0 intersects y-axis at a point P. ∵ the x coordinate of P is 0.

### What is the general equation of a curve?

The equation x + y = 1 represents a straight line in the cartesian plane, as shown in the picture below. Hence, an equation of a curve is the equation that can be used to represent the curve in a standard coordinate system.

How do you calculate the tangent of a curve?

Using the power rule,the first derivative f ′ ( x) = 3 x 2+4 x+5 {\\displaystyle f’ (x)=3x^{2}+4x+5} .

• Since x = 2,find f ′ ( 2) = 3 ( 2) 2+4 ( 2)+5 = 25 {\\displaystyle f’ (2)=3 (2)^{2}+4 (2)+5=25} .
• Notice we do not have a point this time,only an x-coordinate.
• #### How do you find the equation of a tangent plane?

Remembering Tangent Lines. Let us first remember what is meant by finding the tangent line for functions of a single variable,f (x).

• Defining Tangents for Multivariable Functions.
• Example of Finding the Tangent Plane.
• Example of Finding the Tangent Hyperplane.
• Conclusion.
• #### How do you calculate tangent angle?

Tangent calculator. The following is a calculator to find out either the tangent value of an angle or the angle from the tangent value.

• Commonly used angles. While we can find tan⁡ (θ) for any angle,there are some angles that are more frequently used in trigonometry.
• Reference angles.
• What is the derivative of a tangent line?

Find the derivative,f ‘ ( x ).

• Plug in x = a to get the slope. That is,compute m = f ‘ ( a ).
• If not already given in the problem,find the y -coordinate of the point.
• Use the point-slope form and solve for y to find the equation of the tangent line.