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Equation of a circle through the points of intersection of two circles and Those of a circle and A straight line

To find the equation of a circle passing through the points of intersection of two circles, we can follow these steps: Let’s say the two circles have equations: (x – a)^2 + (y – b)^2 = r^2 (x – c)^2 + (y – d)^2 = s^2 where (a,b) and (c,d) are the centers of the…

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Incentre and circumcentre of a triangle

Circumscribed circle In calculation, the encompassed circle or circumcircle of a polygon is a circle that goes through all the vertices of the polygon. The focal point of this circle is known as the circumcenter and its range is known as the circumradius. Few out of every odd polygon has an encompassed circle. A polygon…

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Orthocentre

In calculation, an orthocentric framework is a bunch of four focuses on a plane, one of which is the orthocenter of the triangle shaped by the other three. Proportionately, the lines going through disjoint matches among the focuses are opposite, and the four circles going through any three of the four focuses have a similar…

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Centroid

In analytical geometry, the centroid of a plane figure is the point where its medians intersect. A median is a line segment connecting a vertex of the figure to the midpoint of the opposite side. The centroid is often referred to as the “center of mass” or “center of gravity” of the figure, as it…

March 29, 2023admin@coaching-center.inCentroid, JEE Mathematics Analytical GeometryCase Study on, Centroid, Centroid 1, List of centroids, Pappus's centroid theorem, Properties, What is Required, White Paper on

Equation of the bisector of the angle between two lines

Suppose we have two lines in a Cartesian coordinate system, given by the equations: a1x + b1y + c1 = 0a2x + b2y + c2 = 0 The angle between these two lines can be found using the formula: tan(theta) = |(m2 – m1)/(1 + m1*m2)| where m1 and m2 are the slopes of the…

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Distance of a point from a line

To find the distance between a point and a line in analytical geometry, you can use the formula: distance = |ax + by + c| / √(a^2 + b^2) where a, b, and c are constants that represent the coefficients of the equation of the line in the form of ax + by + c…

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Distance between two points

In analytical geometry, the distance between two points in a plane is given by the distance formula: 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. To use the formula, simply substitute the values of…

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Trigonometric functions

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions can be defined in terms of the sides of a right triangle as follows: In addition to these three functions,…

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Standard deviation and variance of grouped and ungrouped data

Standard deviation and variance are measures of variability that provide information about how spread out a dataset is. The standard deviation is the square root of the variance, and it measures the average deviation of each data point from the mean. In general, the larger the standard deviation or variance, the more spread out the…

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Mean deviation

Mean deviation is a measure of variability that describes the average difference between the values in a dataset and their mean. It is also known as mean absolute deviation (MAD). The formula for calculating the mean deviation is: Mean Deviation = (Σ |xi – x̄|) / n where: Σ represents the sum of the absolute…

March 28, 2023admin@coaching-center.inJEE Mathematics Probability and Statistics, mean deviationCase Study on, How is Required, Mean deviation, What is Required, When is Required, Where is Required, White Paper on, Who is Required

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