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What is the shape of the curve obtained when all points are at equal distance from a center?
A curve is a smooth continuous line that bends without sharp angles. It can represent various shapes such as circular or parabolic forms. In mathematics a curve is often used to model relationships between variables or to describe paths in geometry or physics. Curves can be open or closed.
In Class 6 Maths Chapter 8 on Playing with Constructions students explore geometric tools such as ruler and compass to make basic constructions. The chapter covers drawing different types of angles perpendicular bisectors and triangles. Students also learn how to use these tools to create geometric shapes and solve problems related to constructions.
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A curve with all points at an equal distance from a fixed center is defined as a Circle. This is because every point (x, y) on the circle satisfies the equation:
(x − x₀)² + (y − y₀)² = r²
where (x₀, y₀) is the center and r is the constant distance (radius) from the center to any point on the circle.
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