Final answer:
To find the equation of a tangent line to a curve, you can use various methods including the point-slope form, the normal vector, the parametric form, or the slope-intercept form.
Step-by-step explanation:
The equation of a tangent line to a curve can be found using various methods:
A) Use the point-slope form: The equation of a tangent line can be written as y - y1 = m(x - x1), where (x1, y1) is a point on the curve and m is the slope of the tangent line.
B) Apply the normal vector: The equation of a tangent line can be written as r(t) = r0 + tN, where r(t) represents a point on the tangent line, r0 represents a point on the curve, t is a parameter, and N is the normal vector to the curve at the point r0.
C) Employ the parametric form: The equation of a tangent line can be written as y = f'(x0)(x - x0) + y0, where (x0, y0) is a point on the curve and f'(x0) is the derivative of the curve at x0.
D) Use the slope-intercept form: The equation of a tangent line can be written as y = mx + b, where m is the slope of the tangent line and b is the y-intercept.