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# Category Archives: NonLinear Equations

## Solving Rational Equations with Polynomials example question

Solve the following Rational Equation provided below:

Solution to this Rational Equation with Polynomials practice problem is given in the video below!

## Equation of a Hyperbola problem example

Analyze and sketch Graph of the Hyperbola:

x2y2 + 6x + 34 = 0

Solution to this Equation of Hyperbola practice problem is provided in the video below!

## Equation of Hyperbola ECCENTRICITY example question #2

Find the Eccentricity of the Hyperbola:

Solution to this Eccentricity of a Hyperbola practice problem is provided in the video below!

## Equation of a Hyperbola example #3

Find the equation of a Hyperbola

(a) with vertices (0, ±12) and asymptotes y = ±3x

(b) with foci (3, 6) and (11, 6) and eccentricity

Solution to this Equation of Hyperbola practice problem is provided in the video below!

## Equation of an Ellipse problem example

Analyze and Sketch the graph of the Ellipse given by

25x2 + 16y2 + 100x – 96y = 156

Solution to this Equation of Ellipse practice problem is provided in the video below!

## Eccentricity of Ellipse example question #2

Find the Eccentricity for

Solution to this Equation of an Ellipse practice problem is provided in the video below!

## Equation of an Ellipse with Vertices and Eccentricity example #3

Find the equation of an Ellipse with

(a) major vertices (±4, 0) and eccentricity

(b) minor vertices (-3, 4) and (1, 4) and eccentricity

Solution to this Equation of Ellipse practice problem is provided in the video below!

## Equation of Ellipse example problem #4

Use the definition of an ellipse PF1 + PF2 = 2a directly to find the equation of an ellipse with foci (0, 0) and (4, 0 ) and major axis 2a = 6.

Solution to this Equation of an Ellipse practice problem is provided in the video below!

## Equation of Parabola problem example

Find Equations for Parabolas in standard position

(a) with Focus at (0, 7) and Directrix the line y = -7

(b) with Focus at (, 0) and Directrix the line x =

Solution to this Equation of Parabola practice problem is provided in the video below!

## Equation of Parabola example question #2

Find the Equation for Parabola in standard orientation with Focus at (-2, 3) and Directrix the line y = 1.

Solution to this Equation of Parabola practice problem is provided in the video below!

## Equation of a Parabola example #3

Use the Definition of the Parabola directly to find the equation of a parabola with Focus F(2, 2) and Directrix the line x + y + 2 = 0.

Solution to this Equation of Parabola practice problem is provided in the video below!

## Loci of Points problem example

Find the locus of points P(x, y) such that the distance from P to the y-axis is 5.

Solution to this Locus of Points practice problem is provided in the video below!

## Locus of Points example question #2

Find the locus of points P(x, y) such that the distance of P from P1(1, 1) is one-half the distance of P from P2(-2, -2).

Solution to this Loci of Points practice problem is provided in the video below!

## Loci of Points example #3

Find the locus of points P(x, y) such that P is equidistant from both axes.

Solution to this Locus of Points practice problem is provided in the video below!

## Locus of Points example problem #4

Find the locus of points P(x, y) such that P is equidistant from (5, -1) and (3, -8).

Solution to this Loci of Points practice problem is provided in the video below!

## Loci of Points example question #5

Find the locus of points P(x, y) such that P is equidistant from (-5, 3) and xy + 8 = 0.

Solution to this hard Locus of Points practice problem is provided in the video below!

## Hard Locus of Points example

Find the locus of points P(x, y) such that the product of their distances from (0, 4) and (0, -4) is 16.

Solution to this Loci of Points practice problem is provided in the video below!

## System of NonLinear Equations problem example

Find Real and Imaginary solutions, whichever exist, to the Systems of NonLinear Equations:

a)

b)

Solution to these Systems of NonLinear Equations practice problems is provided in the video below!

## HARD System of NonLinear Equations example question

Determine Real and Imaginary solutions, whichever exist, to the given System of NonLinear Equations:

Solution to this Hard System of NonLinear Equations practice problem is provided in the video below!

## VERY HARD System of NonLinear Equations example

Solve the System of NonLinear Equations provided below:

Solution to this Very Hard System of NonLinear Equations practice problem is provided in the video below!

## HARDEST System of NonLinear Equations example problem

Find the solutions to the System of NonLinear Equations provided below:

Solution to this Most Difficult System of NonLinear Equations practice problem is provided in the video below!

## NonLinear System of Equations Word Problem

A rectangle of perimeter 100 meters is to be constructed to have area 100 square meters. What dimensions are required?

Solution to this NonLinear System of Equations word practice problem is provided in the video below!

## Exponential Equations example question

Solve the following Exponential Equation:

Solution to this Exponential Equation practice problem is provided in the video below!

## Exponential Equation example problem

Solve the Exponential Equation provided below:

Solution to this Exponential Equation practice problem is provided in the video below!

## Exponential Equations example

Find solutions to the given Exponential Equation:

Solution to this Exponential Equation practice problem is provided in the video below!

Solve the following Quadratic Equations by

a) Factoring

b) Completing the Square