Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes using coordinates. It is also known as analytic geometry, and it was developed by RenĂ© Descartes in the 17th century. Coordinate geometry is used extensively in many fields, including physics, engineering, and computer graphics.

**General Equation of Second Degree**

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**Transformation of Coordinates**

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**Plane**

**Three Dimensional Coordinate System**

**Conicoide**

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The key components of coordinate geometry include:

- Cartesian coordinate system: The Cartesian coordinate system is a two-dimensional plane consisting of two perpendicular number lines, the x-axis and y-axis, that intersect at a point called the origin. Each point on the plane can be identified by a unique ordered pair (x, y) that represents its distance from the origin in the horizontal (x) and vertical (y) directions.
- Distance formula: The distance formula is used to calculate the distance between two points in the coordinate plane. It is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

- Midpoint formula: The midpoint formula is used to calculate the midpoint between two points in the coordinate plane. It is given by:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

- Slope: Slope is a measure of the steepness of a line, and it is calculated by dividing the change in y by the change in x. The slope formula is given by:

m = (y2 – y1)/(x2 – x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

- Equations of lines: The equation of a line in the coordinate plane can be written in various forms, including slope-intercept form, point-slope form, and standard form. The slope-intercept form is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

- Conic sections: Conic sections are curves formed by the intersection of a plane with a cone. The four types of conic sections are the circle, ellipse, parabola, and hyperbola. The equations of these curves can be derived using the principles of coordinate geometry.

Overall, coordinate geometry provides a powerful tool for the study of geometric shapes and their properties. It allows us to express geometric concepts and relationships in terms of algebraic equations, and to visualize these concepts using the coordinate plane.