Insertion of Arithmetic Mean (AM) between Two Numbers Arithmetic progression (AP): A sequence is said to be an arithmetic progression, if the difference of a term and previous term is always same. i, e.., an₊₁ – an = constant (d) The constant difference, generally denoted by ‘d’ is called the common difference. Example: (i) 1, Read more about Insertion of Arithmetic Mean (AM) between Two Numbers[…]
Circles – Inverse Points Let S = 0 be a circle with center C and radius r. two points P, Q are said to be inverse points with respect to S = 0 if. 1. C, P, Q are collinear 2. P, Q lies on the same said of C 3. CQ = r² Note: Read more about Circles – Inverse Points[…]
Applications of First Order Differential Equation Growth and Decay: Let N(t) denote the amount of substance (or population) that is either growing or decaying. If we assume that , the time rate of change of this amount of substance, is proportional to the amount of substance present, then or . Where, k is the constant Read more about Applications of First Order Differential Equation[…]
Application of derivatives – Normal Normal: The normal to the curve at any point P on it is the straight line which passes through P and is perpendicular to the tangent to the curve at P. Slope of Normal: We know that normal to the curve at P (x₁, y₁) is a line perpendicular to Read more about Application of derivatives – Normal[…]
System of Planes An equation of the plane contains three independent constants as such a plane is uniquely determined by three independent conditions. If we consider a plane satisfy just two given conditions, its equation will contain one arbitrary constant. If we consider a plane satisfy one condition.it equations contain two arbitrary constants We have Read more about System of Planes[…]
Applications of differentiation – Errors and Tangent Errors Definition: let y = f(x) be a function defined in neighborhood of a point x. Let δx be a small change in x and δy be the corresponding change in y. If δx is considered change in y. i) δy is called the absolute error or error Read more about Applications of differentiation – Errors and Tangent[…]
Length of the Latus Rectum and Parametric Equation of Chord Length of the Latus Rectum: The length of the latus rectum of the parabola y² = 4ax is 4a Proof: Let LL’ be the length of the latus rectum of the parabola y² = 4ax Let SL = I, then L = (a, l) Since L is a Read more about Length of the Latus Rectum and Parametric Equation of Chord[…]
Parabola – Conormal Points and Pair of Tangent Conormal Points: The points on the parabola through which normal drawn are concurrent i.e., pass through the same point are called conormal points. The conormal points are also called the feet of the normal. Points A, B, C in which the three normal from P (h, k) meet the Read more about Parabola – Conormal Points and Pair of Tangent[…]
Position of the Point with respect to the Parabola Let S ≡ y² = 4ax be the equation of the parabola and P(x₁, y₁), be any in the region of the parabola, then S₁ ≡ y₁² – 4ax₁. The point (x₁, y₁) lies outside, on or within the parabola y² = 4ax according as S₁ Read more about Position of the Point with respect to the Parabola[…]
Ellipse – Normal Definition: Let S = 0 be an ellipse and P be a point on the ellipse S = 0. The line passing through P and perpendicular to tangent of S = 0 at P is called the normal to the ellipse S = 0 at P. Theorem: The equation of the normal Read more about Ellipse – Normal[…]