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# Plane Curve

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 Sub Topics In Geometry, we deal with many types of shapes and figures like lines, circles, ellipses, curve and many more. They all come under the family of curves. In geometry, there are two types of curve: 1. Open curve: In open curve, we consider those curves whose end points never meet together. 2. Close curve: Close curve are types of curve whose closing points are connected or joined. Equation of curve which is given as: y = x2, here ‘y’ denotes the y – coordinates value and ‘x’ denotes the x – coordinate values. We can also write equation of curve using parameter of curves and these equations are called parametric equation of curve. Let’s talk about curves in geometry. Basically curves are of two types: 1. Analytic Curve: - These are easy curves so that they can be managed by an equation such as ellipse, straight line and helices. 2. Interpolated Curve: - A ll B - spline curves are considered as interpolated curve. As we know curve can be use in two -dimensional (plane curves) curve and three-dimensional (space). A curve in two-dimensional is also called as “plane curve” that lies in a single plane. It may be closed or open. It is a curve in a real Euclidean plane R2. A smooth plane curve can be represented by an equation ƒ(x, y) = 0, here ƒ: R2 -> R. It is a smooth function. Some of plane curves are inside curves which are known as interior curves and curves which are outside the curve are known as exterior curves. In spite of these curves, some are on edges (means on boundary) which are known boundary curves. Examples: Straight line ax + by = c Parabola y – x2 = 0 Circle x2 + y2 = r2 (here r is the radius of the Circle) Ellipse x2 / (a2 + y2) / b2 = 1.