Relation: For any non-empty sets A and B, a subset of A × B is called a relation from A to B. Example: A relation assigns the x’s with y’sThis relation can be written as {(1, 6), (2, 2), (3, 4), (4, 8), (5, 10)} Example: A x B = {{a, x), (b, x), (c, x), (a, Read more about Relations and Functions[…]
Sir Isaac Newton gave a mathematical relation to calculate the force of gravitation and this relation is known as the universal law of gravitation. It is a common belief that an apple fell on Newton’s head and he realized that gravity exists. This isn’t completely incorrect. But Newton already knew about the existence of gravity. Read more about Universal Law of Gravitation[…]
In three dimensions, the coordinate axes of a rectangular Cartesian co-ordinate system are three mutually perpendicular lines. The axes are called the x, y and z axes. Co-ordinates of a Point: The coordinates of a point P in three-dimensional geometry is always written in the form of triplet like (x, y, z). Here x, y Read more about Three-Dimensional Geometry[…]
This is applicable only to a plane lamina. The moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about any two mutually perpendicular axes, passing in its own plane, intersecting each other at the point through which Read more about Perpendicular Axis Theorem[…]
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse.Conic section consists of those points whose distances to some point (called focus) and some line (called directrix) are in a fixed ratio, called the eccentricity. Read more about Conic Sections[…]
The theorem determines the moment of inertia of a rigid body about any given axis, given that moment of inertia about the parallel axis through the centre of mass of an object and the perpendicular distance between the axes. The moment of inertia of a body about an axis is equal to its moment of Read more about Parallel Axis Theorem[…]
As per the directions of the Government, Karnataka Examinations Authority is conducting the Common Entrance Test – 2018 as per the following schedule for admission to the First year or First semester Engineering, Technology, Farm Science courses i.e., courses i.e., Bachelor of Veterinary Science and Animal Husbandry (B.V.Sc. & A.H.), B.Sc. (Agriculture), B.Sc. (Sericulture), B.Sc Read more about Karnataka – Common Entrance Test (K-CET) 2018 Time Table[…]
The locus of the point of intersection of the tangents which are at right angles is known as the director circle of the hyperbola. . The equation to the director circle is x² + y² = a² – b².Example: Hyperbola 9x² – 16y² = 144 then find the equation of the director circle. Solution: The Read more about Director Circle of the Hyperbola[…]
Friction is a force that tries to oppose motion between the two surfaces in placed contact. When we throw a ball on the floor it starting with some velocity. But once it is rolled ideally no force is acting in the direction of motion and according to Newton’s first law the ball should keep on Read more about Friction[…]
Auxiliary circle of an ellipse which is a circle described on the major axis of an ellipse as its diameter. Let the ellipse be … (1)Then the equation of its auxiliary circle is x² + y² = a² … (2) Take a point P(x₁, y₁) on (1). Through P, draw a line perpendicular to major axis intersecting major axis in N and auxiliary Read more about Auxiliary Circle of an Ellipse […]