The standard equation of the circle is – (x-h)2 + (y-k)2 = r2. Here h and k are the center coordinates of the circle and ‘r’ denotes the radius of the circle.
In order to understand the derivation of the circle, we should first focus on ‘what is a circle?’ A circle is the set of all the points which are being equally placed for a fixed point on the plane surface. This center of the circle is actually the fixed point here. The circumference of the circle is the boundary of the circle. So, any point on the circumference and the distance between the center is denoted by ‘r’ which is the radius of the circle.
With this basic knowledge about the circle, let us proceed with the discussion of the equation of the circle.
Equation of a Circle
As already discussed, the circle is a closed figure with a fixed point called the central part of the circle. In a circle, all the points on the boundary or the circumference are at equal distance to the central or radius of the circle. The equation of the circle with h and k coordinates is – (x-h)2 + (y-k)2 = r2. So, if we know the coordinates of the central part of the circle (when placed on a graph paper) and the radius as well then we can easily find out the equation of the circle.
Did You Know?
- The circles are known as congruent circles if all the circles have equal radii.
- The diameter of the circle is known as the longest chord of the circle.
- The radius which is being drawn perpendicular to the chord of the circle bisects the chord.
- Even if the radius of the circle is different, still the circle will be similar.
- A circle can cover a rectangle, trapezium, triangle, square, and kite which is the rhombus.
What is the Equation of Line?
The equation of the line can be algebraically defined as representing the set of points that are being represented on the line segment. They form the coordinate line in the coordinate system. There are various points that make the coordinate axis, they are represented by variables x and y – this is done to form the algebraic equation. With the help of the equation of the line, we can check if the line is lying on a line or not.
Formation of the Equation of Line
The equation of the line is formed with the help of the slope of the line and with the help of the definite point on the line. To understand the equation of the line with more clarity, we will discuss the slope of the line and its inclination of the line. The slope of the line and the inclination of the line make a positive axis with the x in its zone. This point refers to the point in the coordinate system with the x and y as its coordinating axis.
So, What did we learn so far? We have learned the basics about Circle and the Line, with their respective equation in detail. The equation of the line and the circle is mainly applied in the field of engineering. A student can score good marks in this part by practicing the sums after they have studied the concept minutely which will be possible with good guidance.
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