Parametric equations and finding tangents from circles

• xllx
In summary, the tangent equation at a point on a circle with parametric equations x=1+2cos\theta and y=3+2sin\theta can be found using the formula y-y1=m(x-x1), where m=-cot\theta and x1=1+2cos\theta and y1=3+2sin\theta.

Homework Statement

A circle has the parametric equations:
x=1+2cos$$\theta$$
y=3+2sin$$\theta$$

dy/dx= -1/tan$$\theta$$

Find the tangent equation at the point with parameter $$\theta$$

y-y1=m(x-x1)

The Attempt at a Solution

I've tried putting dy/dx in as the gradient and then x1 and y1 as the parametric equations but i seem to come up with some really long equation that I am sure isn't right.

Any help at all would be greatly appreciated. Many thanks.

You mean you don't think this is right?:

$$y-3-2sin\theta=-cot\theta(x-1-2cos\theta)$$

Because it is :tongue:

1. What are parametric equations?

Parametric equations are a set of equations that express a set of quantities as functions of one or more independent variables, known as parameters. These equations are commonly used to describe the motion of objects in space and are often written in terms of time, with the parameters representing the coordinates of the object at a specific time.

2. How are parametric equations used in finding tangents from circles?

Parametric equations are used in finding tangents from circles by representing the coordinates of the circle as functions of a parameter. The tangent to the circle at a specific point can then be found by finding the derivative of the parametric equations at that point.

3. What is the process of finding tangents from circles using parametric equations?

The process of finding tangents from circles using parametric equations involves representing the circle as a set of parametric equations, finding the derivative of these equations, and setting it equal to the slope of the tangent line. The point of tangency can then be found by solving for the value of the parameter.

4. Can parametric equations be used to find tangents from circles with varying radii?

Yes, parametric equations can be used to find tangents from circles with varying radii. The equations used will depend on the center and radius of the circle, but the general process of finding the derivative and setting it equal to the slope of the tangent line remains the same.

5. Are there any limitations to using parametric equations in finding tangents from circles?

One limitation of using parametric equations in finding tangents from circles is that the equations may become more complex for circles with irregular shapes or for cases where the center of the circle is not at the origin. In these cases, alternative methods such as using the distance formula or the Pythagorean theorem may be more suitable.