equation of ellipse

Let us learn about equation of ellipse

Equation of ellipse in standard form

[ x²/a² ] + [ y²/b² ] = 1

Let x'ox & yoy' be the co-ordinate axes.

Let F(c, o) and f'(- c, o) be 2 given fixed points .

Let us consider the locus of a point which moves in such a way that the sum of its distances from F & F' remains constant say equal to 2a where a > c.

Let P(x, y) be any point on the locus.

Then
PF + PF' = 2a

=> √[(x - c)² + y²] + √[(x + c)² + y²] = 2a
√[(x + c)² + y²] = 2a - √[(x-c)² + y²]

On squaring both sides,

we get
[(x + c)² + y²] = 4a² + (x - c)² + y² - 4a√[(x - c)² + y²]
[(x + c) ² - (x - c) ²] - 4a² = - 4a √[(x - c)² + y²]
4 x c – 4a² = - 4a √[(x - c)² + y²]
√[(x - c)² + y²] = a – (c/a) x

Again squaring on both sides ,

we get
(x - c)² + y² = a² + [c²x²/a²] - 2cx
x² - [c²x²/a²] + y² = a² - c²
x² [1 – (c²/a²)] + y² = a² - c²
[x²(a² - c²)] / a² +y² = a² - c²

Dividing by (a² - c²)

we get
(x²/a²) + (y²/(a²- c²)) = 1
(x²/a²) + (y²/b²) = 1 , where b² = a² - c²

Thus (x²/a²) + (y²/b²) = 1 is the required equation of an ellipse in standard form

In our next blog we shall learn about relative molecular mass I hope the above explanation was useful.Keep reading and leave your comments.

square root rules

Let us learn about square root rules

• The product of 2 values in the square root is always having various values in it, & then it can be rewrite in the form as like, the 2 radical values are written inside a single radical.

• The number always lies outside radical symbol, if the number lies outside the radical is squared before it taken into the radical.

• The radical existing in fraction value then it can be written in individual roots, as like a separate radical in denominator & a separate radical in numerator.

• When ever a perfect square comes out from the square root, then the root of that perfect square is negligible.

In our next blog we shall learn about feet symbol I hope the above explanation was useful.Keep reading and leave your comments.

boolean calculator

Let us learn about boolean calculator

Student can enter a formular like "a & b & (not c)" & it shows you a table where you can see on which Boolean combination of a, b & c the term is true. Boolean logic algebra is the algebra of 2 values. These values are generally taken to be 0 & 1, as we shall do here, although F & T, false & true, etc. Boolean logic algebra is also a common uses of Boolean logic calculator. More basically Boolean algebra is algebra of values from any Boolean algebra as a model of the laws of Boolean algebra. In Boolean calculator first enter the expression then enter the values of x and y. now press the calculate button then the solution will be produced.

In our next blog we shall learn about maintenance test questions I hope the above explanation was useful.Keep reading and leave your comments.

quadrants on a graph

Let us learn about quadrants on a graph

The quadrants on a graph are referred as any of the 4 equal areas made by dividing a plane by an x & y axis

The x- & y- axes divide the coordinate plane into 4 regions. These regions are said to be as the quadrants.

Quadrant is the word helps us define the parts. If you draw straight & perpendicular lines, divide the page into 4 parts, each part is called a quadrant graph. The Quadrants of Performance concept begins with a basic graph that plots 2 major thresholds

In our next blog we shall learn about quantum mechanical model of the atom I hope the above explanation was useful.Keep reading and leave your comments.

angle of elevation and depression

Let us learn about angle of elevation and depression

In order to find solution for problems involving angles of elevation & depression, it is important to

* Always use basic right triangle trigonometry

* solve equations which involve 1 fractional term is also necessary to know.

* Try to find an angle that is given a right triangle ratio of sides.

* The statement that corresponding angles formed by parallel lines have the same measure.

A distinctive problem of angles of elevation & depression involves organizing information regarding distances & angles within a right triangle. In some other cases, learner will be asked to determine the measurement of an angle; in others, the problem might be to find an unfamiliar distance.

In our next blog we shall learn about animals and their young ones I hope the above explanation was useful.Keep reading and leave your comments.

mental ability questions with answers

Let us learn about mental ability questions with answers

If student take interest to find solution of math given problems, they can improve their mental ability.

1. Write five prime numbers between 50 and 75.

Solution: 53, 59, 61, 67, 71

2. Every prime number is odd except

Solution: 2

3. What should be added to 40.09 to make it 51 dollars?

Solution: 10.91 dollars

Math is the ability to perform arithmetic calculations without the help or aid of external computing tools. Math test require more & more background knowledge & ability in math basic skills.

In our next blog we shall learn about help math I hope the above explanation was useful.Keep reading and leave your comments.

equation of a line from two points

Let us learn about equation of a line from two points

If Students are given 2 points, how can they find the equation of the line passing through the 2 points? If student know the slope & a point (x₁, y₁) student have that

rise y - y₁
m = =
run x - x₁

Now multiplying by

x - x₁

equation of a line from two points Point Slope Formula for the Equation of a Line

y - y₁ = m (x - x₁)

Find the equation of line from the point (1,2) with slope 4.

Solution:

We use the formula:

y - 2 = 4(x - 1) = 4x - 4 Therefore y = 4x - 4 + 2 = 4x - 2.

In our next blog we shall learn about how to calculate ratios I hope the above explanation was useful.Keep reading and leave your comments.