Table of Contents
How many tangent lines pass through a point?
There are 2 tangent lines that pass through the point (1,2) .
How do you find the equation of a graph with two lines?
Steps to find the equation of a line from two points:
- Find the slope using the slope formula.
- Use the slope and one of the points to solve for the y-intercept (b).
- Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
How many tangent line passes through a point?
Axiomatically, through any two points, there is exactly one line. By the definition of tangency, a line that is tangent to a curve touches that curve at exactly one point.
Is (y – 3) = -2(x – 4) a tangent line?
Tangent line definition is a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point. So here even though (y − 3) = − 2 (x − 4) satisfies line equation but since it crosses curve at (4, 3) its not a tangent line.
What is the slope of the tangent line at point 4-3?
So at point ( 4, 3) the slope of the tangent line is d y d x = t = 1. Our tangent line then is y = x − 1. However, it can be shown through the elimination of x and y from the tangent line equation that y = − 2 x + 11 is also tangent to the curve and passes through ( 4, 3).
What is the gradient of the tangent of the parabola?
The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. So for our curve (the parabola) we have Let P (α,β) be any generic point on the curve. Then the gradient of the tangent at P is given by:
What is the gradient of the tangent of a curve?
A generic point on the curve can be represented by (a,f (a)), ie (a,a2), and the gradient of the tangent at that point has gradient m = f ‘(a), or m = 2a, This is a quadratic in a (which is good as we expected to find two equation, and therefore we require two values of a !)