mathemerize

Family of Lines – The combined Equation of Angle Bisectors

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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Equation of Straight Lines in all Forms

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 …

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Formula for Angle between Two Lines

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 …

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Common Tangent to Two Circles – Direct and Transverse

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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Properties of Inverse Trigonometric Functions with Example

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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Inverse Trigonometric Function Class 12 – Domain & Range

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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