GRADE 4TH TO BACHELOR CLASSES (BA/B.Sc./B.E./B.TECH.) and other Engineering Courses.

MATHEMATICS – 10, 20, 20-1, 30, 30-1, 31, 100, 101, 102, 113, 114, 115, 120 AND 125.

Algebra – Linear, Radical, Quadratic, Monomial/Binomial/Polynomial, Exponential, Logarithmic, Rational, and Trigonometric Equations, Algebraic and Graphic expressions, relations, and functions and more .

Trigonometry – Trigonometry equations, Trigonometric functions, and Trigonometric ratios etc.

Calculus – Differential Calculus, Integral Calculus, Derivatives, Differential Equations, Integral Equations and more.

Determinants and Matrices, Vectors and Vector space, Rank, Eigenvalues and Eigenvectors, and more.

Straight Line and Geometry – Point formula, distance formula, mid-point formula, section formula, Angles and Area of Triangles, Two Dimensional and Three Dimensional Geometry and more.

Co-ordinates and Solid Geometry – Coordinates, Planes, Coordinate Systems : One Dimensional, Two Dimensional and Three Dimensional, Area and Perimeter of Polygons, Transformation and Rotations, Equations of Curves, circles, and Ellipses, Parabola, Hyperbola, and more.

Statistics – Mean, Median, Mode, Co-relation, rank, rank of co-relation, Deviations, mean deviation, standard deviation and more.   An ellipse can be defined as the locus of all points that satisfy the equation x^2 / a^2 + y^2 / b^2 = 1

where:

x,y are the coordinates of any point on the ellipse,

a, b are the radius on the x and y axes respectively

PARAMETRIC EQUATION OF AN ELLIPSE An ellipse can be defined as the locus of all points that satisfy the equations

x = a cos t

y = b sin t

where:

x,y are the coordinates of any point on the ellipse,

a, b are the radius on the x and y axes respectively,

t is the parameter, which ranges from 0 to 2π radians.

This equation is very similar to the one used to define a circle, and much of the discussion is omitted here to avoid duplication.

The only difference between the circle and the ellipse is that in a circle there is one radius, but an ellipse has two:

• One radius is measured along the x-axis and is usually called a.

• The other is measured along the y-axis and is usually called b.

x^2 + y^2 = 0, Circle x^2 + y^2 = r^2.

Ellipse x^2 / a^2 + y^2 / b^2 = 1, Ellipse x^2 / b^2 + y^2 / a^2 = 1,

Hyperbola x^2 / a^2 – y^2 / b^2 = 1. Parabola 4px = y^2 