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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.
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:
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.
Find the tangent equation to the parabola x_2 = 20y at the point (2, -4):
$$ X_2 = 20y $$
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: \(x = 4y – 3\).
Determine the equation of tangent line at y = 5.
$$ f (y) = 6 y^2 – 2y + 5f $$
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:
$$ x = 93 + 46y – 184$$
$$ x = 46y – 91$$
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.
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.
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.