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
The text passage provides an overview of various mathematical topics and equations, including definitions and parametric equations for an ellipse, and equations for other conic sections like circles, hyperbolas, and parabolas. It does not contain any specific mathematical questions or answers.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
user
The text passage provides an overview of various mathematical topics and equations, including definitions and parametric equations for an ellipse, and equations for other conic sections like circles, hyperbolas, and parabolas. It does not contain any specific mathematical questions or answers.

TYPE: NO_QUESTION