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 […]
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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 :
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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
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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,
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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
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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
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This tutorial is for you if you are searching for – “Definition of Continuity of a function, Discontinuity and Missing Point Discontinuity.” Let’s begin – Continuous Functions A Function for which a small change in the independent variable causes only a small change and not a sudden jump in the dependent variable are called continuous
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Here, you will learn differentiability of a function and differentiability at a point and over an Interval. Let’s begin – Meaning of Derivative The instantaneous rate of change of a function with respect to the dependent variable is called derivative. Let ‘f’ be a given function of one variable and let \(\Delta\)x denote a number
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Here, you will learn Different Types of Parabola and Standard equations of parabola, focal chord, double ordinate and latus rectum of parabola. Let’s begin – What is Parabola ? A parabola is the locus of a point which moves in a plane, such that its distance from a fixed point(focus) is equal to its perpendicular
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Here, you will learn general equation and formulas for conic sections and formula to distinguish between conic. Conic Sections A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed
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