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.
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.
