Here, you will learn probability basic concepts and definitions of probability. Let’s begin – Probability gives us a measure of likelihood that something will happen. However probability can never predict the number of times that an occurrence actually happens. Probability Basic Concepts and Definitions (a) Experiment : An action or operation resulting in two or …
Here, you will learn equation of family of lines and the combined equation of the bisectors of the angle between the lines. Family of Lines Equation If equation of two lines be P = \(a_1x+b_1y+c_1\) = 0 and Q = \(a_2x+b_2y+c_2\) = 0, then the equation of the lines passing through the point of intersection …
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Here, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc. Let’s begin – A relation between x and y which is satisfied by co-ordinates of every point lying on a line is called equation of the straight lines. Here, remember that every one …
Here, you will learn formula for angle between two lines, equation of straight line making an angle with a given line and reflection and image of a point in a line and also length of perpendicular from a point on a line. Let’s begin – Angle between Two Lines (a) If \(\theta\) be the angle …
Here you will learn equation of family of circles with examples. Let’ begin – Family of Circles (a) The equation of the family of circles passing through the point of intersection of two circles \(S_1\) = 0 & \(S_2\) = 0 is : \(S_1\) + K\(S_2\) = 0 (K \(\ne\) -1) (b) The …
Here you will learn common tangent to two circles i.e direct and transverse common tangents to two circles. Let’s begin – Common Tangent to Two Circles Let two circles having centers \(C_1\) and \(C_2\) and radii, \(r_1\) and \(r_2\) and \(C_1\)\(C_2\) is the distance between their centres then : (a) Both circles will touch : …
Common Tangent to Two Circles – Direct and Transverse Read More »
Here, you will learn equation of asymptotes of hyperbola and how to find the asymptotes of the hyperbola and the director circle of hyperbola. Let’s begin – Equation of Asymptotes of hyperbola If the length of the perpendicular let fall from the point on the hyperbola to a straight line tends to zero as the …
Equation of Asymptotes of Hyperbola – Director Circle Read More »
Here, you will learn all the properties of inverse trigonometric functions class 12 with examples. Let’s begin – Properties of Inverse Trigonometric functions Property – 1 (i) y = \(sin^{-1}(sinx)\), x \(\in\) R, y \(\in\) (-\(\pi\over 2\), \(\pi\over 2\)) periodic with period \(2\pi\)and it is an odd function. (ii) y = \(cos^{-1}(cosx)\), x \(\in\) R, …
Properties of Inverse Trigonometric Functions with Example Read More »
Here, you will learn domain and range of inverse trigonometric function class 12. Let’s begin – Inverse Trigonometric Function The inverse trigonometric functions, denoted by \(sin^{-1}x\) or (arc sinx), \(cos^{-1}x\) etc., denote the angles whose sine, cosine etc, is equal to x. The angles are usually smallest angles, except in case of \(cot^{-1}x\) and if …
Inverse Trigonometric Function Class 12 – Domain & Range Read More »
Here, you will learn intermediate value theorem example and statement and single point continuity. Intermediate Value Theorem Example with Statement Statement : Suppose f(x) is continuous on an interval I, and a and b are any two points of I. Then if \(y_0\) is a number between f(a) and f(b), there exist a number c …
Intermediate Value Theorem Example and Statement Read More »
