Question

How do you know if a line is tangent to a curve?

Answer 1

in order to find whether a line is a tangent to a curve we will solve both the equation, the equation of line and the equation of the curve. If we got one solution after solving the equation then the line is tangent to the given curve but if we got two or more solutions then the line intersects the curve at two or more points.

Complete step by step answer:
The above question belongs to the concept of tangent line two a curve. A tangent is a line which touches the curve at one point. Graphically it means the instantaneous rate at which the curve changes. The slope of the tangent line is given by the derivative of the function at the given point. Therefore, in other words we can say that by finding the derivative of a function at a given point we can get the slope of the tangent line.
Now if a line is tangent to the curve then it must intersect with the curve at one point. In order to check this, we will solve both the equations simultaneously to get the solution. if we get one solution then the given line is tangent to the curve.
An example of any curve and the tangent to the curve is as below,

Note:
The other method to solve the question is by first finding the derivative of the given curve at the point of intersection. The derivative gives the slope of the tangent at that point. If the slope of the given equation is equal to the value of the derivative then the given equation is tangent to the curve.