An ellipse is the locus of a point that moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed straight line is always constant and is always less than unity.

The constant ratio is denoted by e and is known as the **eccentricity** of the ellipse.

If S is the **focus**, ZZ1 is the **directrix** and P is any point on the ellipse, then the definition

SP/PM = e

Find the equation of the ellipse whose focus is (1, 0) and directrix is x + y + 1 = 0.

Let S(1, 0) be the focus, ZZ^{1} be the directrix and the point P(x,y) be any point on the ellipse.

PM = perpendicular from P onto the directrix then

SP/PM = e

1. Find the equation of the ellipse where

a. |
Focus is (-1, 1) Directrix x - 2y + 3= 0 and e = 1/3 |

b. |
Focus is (-2, 3) Directrix is 2x + 3y + 4 = 0, e = 4/5 |

c. |
Focus is (1, 2) Directrix is 3x + 4y - 5 = 0, e = 1/2 |

**a. Solution**

**b. Solution**

Given that the focus S = (-2,3)

Directrix is 2x + 3y + 4= 0

e = 4/5

If P(x,y) is a point on the ellipse

PM = perpendicular from P onto the directrix

**Cross-multiplying**

**c. Solution**

Focus = (1, 2) = S

Directrix is 3x + 4y - 5 = 0

Eccentricity e = 1/2

If P(x,y) be a point on the ellipse

PM = perpendicular from P onto the directrix

- Absolute Values
- Adding and Subtracting Fractions
- Addition of Decimals
- Algebra Linear Equations
- Algebra Quadratic Equations
- Algebra Simultaneous Equations
- Algebraic Properties
- Algebraic Function
- Analyzing and Integrating
- Asymptotes
- Bar Graphs
- Basics of Statistics
- Circular Permutations
- Combinations
- Complex Numbers
- Complex Numbers AddSub
- Complex Numbers Division
- ComplexNumbers Multiplication
- Complex Numbers Properties
- Composite Functions
- Cube and Cube Roots
- Data collection Add Multipli Rules
- Datacollection GroupedMean
- Datacollection Mean
- Datacollection Median
- Datacollection Mode
- Datacollection Probabilitybasics
- Datacollection Probabilityevents
- Dividing Rational Numbers
- Division of Decimals
- Domain of SquareRootFunction
- EquationsReducibleQuadratic
- Exponential Functions
- ExponentialLogarithmicFunction
- Factorization
- FactorizationAnyQPolynomial
- FactorizationMonicQPolynomial
- Fractions & Decimal Conversion
- Functions
- Geometry Basics
- Graph of Rational Functions
- Graph of SquareRootFunction
- GraphicalRepresentation
- Graph of Complex Numbers
- Graphs Functions
- HighestCommonFactor
- Inequalities
- Inverse Square Functions
- Inverse of a Function
- Justifying Solutions
- LeastCommonMultiple
- Linear Equations2Variables
- LinearEquations3Variables
- Linear Equation System
- Linear Equation Graphs
- Linear Inequalities Graphs
- Maxima Minima Zeros
- More Functions
- Multiplication of Decimals
- Multiplying Rational Numbers
- Multiplying Two Polynomials
- Other Functions
- Permutations
- Pictorial BarChart
- Pictorial Bivariatedata
- Pictorial BoxPlots
- Pictorial FrequencyTable
- Pictorial Histogram
- Pictorial LineCharts
- Pictorial PieChart
- Pictorial StemLeafPlot
- Polynomials Addition
- Polynomials Division
- Polynomials Multiplication
- Predicting Values
- Problem Solving Strategies
- Quadratic Equation
- QuadraticEquationsFormula
- QuadraticEquationsSolutions
- QuadraticInequalities
- Rational Behind Functions
- Rational Expression
- Rational Functions
- Real Numbers
- Reciprocal Functions
- Recursive Multiplication
- Rational Numbers
- Review of functions
- Review of Sets and Relations
- Rounding Numbers
- Scientific Notation
- Simple Probabilities
- SimplifyingRationalExpressions
- SolutionQuadratEquawhen
- Solving Fractions
- SolvingQuadraticEquations
- Square of a Binomial
- SquareRootFunctions
- SquareRootFunInequalities
- Squares and Square Roots
- Step Function
- Subtraction of Decimals
- Types of Functions
- Unit Conversions Measurements
- WordProblemsQE