Tangent Line Calculator

An online tangent line calculator will help you to determine the tangent line to the implicit, parametric, polar, and explicit at a particular point. Apart from this, the equation of tangent line calculator can find the horizontal and vertical tangent lines as well.

What is a Tangent Line?

The line and the curve intersect at a point, that point is called tangent point. So, a tangent is a line that just touches the curve at a point. The point where a line and a curve meet is called the point of tangency.

Tangent Line Formula

Well, there are various variables used to determine the equation of the tangent line to the curve at a particular point:

• The slope of a tangent line
• On the curve, where the tangent line is passing

So the Standard equation of tangent line: $$ y – y_1 = (m)(x – x_1)$$ Where (x_1 and y_1) are the line coordinate points and “m” is the slope of the line. Example: Find the tangent equation to the parabola x_2 = 20y at the point (2, -4): Solution: $$ X_2 = 20y $$ Differentiate with respect to "y": $$ 2x (dx/dy) = 20 (1)$$ $$ m = dx / dy = 20/2x ==> 5/x $$ So, slope at the point (2, -4): $$ m = 4 / (-4) ==> -1 $$ Equation of Tangent line is: $$ (x - x_1) = m (y - y_1) $$ $$ (x - (-4)) = (-1) (y - 2) $$ $$ x + 4 = -y + 2 $$ $$ y + x - 2 + 4 = 0 $$ $$ y + x + 2 = 0 $$ When using slope of tangent line calculator, the slope intercepts formula for a line is: $$ x = my + b $$ Where “m” slope of the line and “b” is the x intercept. So, the results will be: $$ x = 4 y^2 - 4y + 1 at y = 1$$ Result = 4 Therefore, if you input the curve "x= 4y^2 - 4y + 1" into our online calculator, you will get the equation of the tangent: \(x = 4y - 3\).

Determining the Equation of a Tangent Line at a Point

Determine the equation of tangent line at y = 5. Solution: $$ f (y) = 6 y^2 - 2y + 5f $$ First of all, substitute y = 5 into the function: $$ f (5) = 6 (5)^2 - 2 (5) + 5 $$ $$ f (5) = 150 - 10 + 5 ==> f (5) = 165$$ by taking the derivative and plug in y = 5: $$ f ' (y) = 12y - 2 $$ $$ f '(5) = 12 (5) - 2 $$ $$ f ' (5) = 58 $$ Then, add both f (5) and f'(5) into the equation of a tangent line, along with 5 for a: $$y = 93 + 46 (y - 5)$$ so the result will be: $$ x = 93 + 46y - 184$$ $$ x = 46y - 91$$

How Tangent Line Equation Calculator Works?

Input:

• Firstly, choose the type of curve either explicit, parametric, or polar from the drop-down list.
• Now, Enter the values of the function
• Then, enter a particular point where you want to find a tangent line
• Click the calculate

Output: 

• Your input and answer 
• Then find the function and take the derivative of a certain function
• Lastly, the calculator determines the slope and the tangent line

FAQs:

Why should we Search Tangent of Function Graphs?

To find a tangent to a graph in a point, we can say that a certain graph has the same slope as a tangent. Then use the tangent to indicate the slope of the graph.

Is Slope of a Tangent Line the Derivative?

The derivative of a function gives the slope of a line tangent to the function at some point on the graph. This will be used to find the equation of a tangent line.

Reference: 

From the source of Wikipedia: Tangent line to a curve, Analytical approach, Intuitive description. From the source of Krista King: What Is The Tangent Line, the tangent line at a particular point, Equation Of The Tangent Line.