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Question

The eccentricity of an ellipse whose centre is at the origin is $1 half space$ If one of its directrices is $x equals negative 4$ then the equation of the normal to it at $open parentheses 1 comma fraction numerator 3 over denominator 2 end fraction close parentheses text end text$ is

$4 x - 2 y = 1$
$4 x + 2 y = 7$
$x + 2 y = 4$
$2 y - x = 2$

The correct answer is: $4 x minus 2 y equals 1$

The given ellipse is depicted in the following figure:

Eccentricity of ellipse is 1/2. Now
$fraction numerator negative a over denominator e end fraction equals negative 4$
That is,
$a equals 4 cross times fraction numerator 1 over denominator 2 end fraction equals 2$
Therefore,
$b to the power of 2 end exponent equals a to the power of 2 end exponent open parentheses 1 minus e to the power of 2 end exponent close parentheses equals a to the power of 2 end exponent open parentheses 1 minus fraction numerator 1 over denominator 4 end fraction close parentheses equals 3$
Hence, the equation of the given ellipse is written as
$fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 3 end fraction equals 1$
$fraction numerator x over denominator 2 end fraction plus fraction numerator 2 y over denominator 3 end fraction cross times y to the power of ´ end exponent equals 0$
$y to the power of ´ end exponent equals fraction numerator negative 3 x over denominator 4 y end fraction$
$open y to the power of ´ end exponent close vertical bar subscript left parenthesis 13 divided by 2 right parenthesis end subscript equals fraction numerator negative 3 over denominator 4 end fraction cross times fraction numerator 2 over denominator 3 end fraction equals fraction numerator negative 1 over denominator 2 end fraction$
Therefore, the equation of normal at $open parentheses 1 comma fraction numerator 3 over denominator 2 end fraction close parentheses text is end text$
$table row cell y minus fraction numerator 3 over denominator 2 end fraction equals 2 left parenthesis x minus 1 right parenthesis end cell row cell 2 y minus 3 equals 4 x minus 4 end cell row cell rightwards double arrow 4 x minus 2 y equals 1 end cell end table$

Find the mean absolute deviation of the given numbers: 6,10,3,3,5,8,6,2

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General

Maths-

Use counter to add -5 + 2, where is + and Is –
Start with:
You add:
Which picture shows the sum:

Maths-General

General

Maths-

The line $∣ x plus m y plus n equals 0 text end text$ is a normal to the ellipse $text end text fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 text end text$ is

Maths-General

General

Maths-

While drawing the map of USA, Jassica represented the distance between two cities as 2cm there the actual distance is 100km. What is the scale of the map.

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General

Maths-

Height of 5 students in a classroom are 125 cm,134 cm, 157 cm,110 cm,146 cm.
Find the range of height

Maths-General

General

Chemistry-

These are the first eight ionization energies for a particular neutral atom. All values are expressed in MJ mol^-1. How many valence electrons do/does this atom possess?

1st

2nd

3rd

4th

5th

6th

7th

8th

1.31

3.39

5.30

7.47

10.99

13.33

71.33

84.01

Chemistry-General

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Maths-

Teacher tells the Class that highest marks obtained by student in her class is twice the lowest marks plus 7 . The highest score is 87 . What is the lowest score?

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General

Maths-

Polly is measuring the temperature of different chemical mixture. The temperature of two mixtures are shown in table as

Which mixture has highest absolute value

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Maths-

Which of the following represents x $greater or equal than$ 4

Maths-General

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Maths-

Janier earns a profit of $2a every day How much money will she earn at a profit at the end of 4 days.

Maths-General

General

Maths-

In a classroom then are 45 students in which 30 are boys are rest are female, find the ratio of number of girls to the number of boys.

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Maths-

Find the area between the two concentric circles of radius 3cm and 4cm.

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Maths-

Which of the following is correct:

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General

Maths-

Lawren has $1000 in a saving account. He wants to save at least $400 before winter. He withdraws $50 every week for daily requirements. Write an inequality that represents Lawren’s situation.

For such questions, we have to see which quantity is constant and variable. We have be careful about the words like “at least”, “at most”, etc.

Lawren has $1000 in a saving account. He wants to save at least $400 before winter. He withdraws $50 every week for daily requirements. Write an inequality that represents Lawren’s situation.

Maths-General

For such questions, we have to see which quantity is constant and variable. We have be careful about the words like “at least”, “at most”, etc.

General

Maths-

A man goes 3 kms east from point A and takes right tum from point B to move 4 kms to point c. What is the minimum distance between paint A and point C

Maths-General

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The eccentricity of an ellipse whose centre is at the origin is If one of its directrices is then the equation of the normal to it at is

The correct answer is:

The given ellipse is depicted in the following figure:Eccentricity of ellipse is 1/2. NowThat is,Therefore,Hence, the equation of the given ellipse is written asTherefore, the equation of normal at

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Find the mean absolute deviation of the given numbers: 6,10,3,3,5,8,6,2

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Use counter to add -5 + 2, where is + and Is –Start with: You add: Which picture shows the sum:

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Teacher tells the Class that highest marks obtained by student in her class is twice the lowest marks plus 7 . The highest score is 87 . What is the lowest score?

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Polly is measuring the temperature of different chemical mixture. The temperature of two mixtures are shown in table asWhich mixture has highest absolute value

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Which of the following is correct:

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Lawren has $1000 in a saving account. He wants to save at least $400 before winter. He withdraws $50 every week for daily requirements. Write an inequality that represents Lawren’s situation.

Lawren has $1000 in a saving account. He wants to save at least $400 before winter. He withdraws $50 every week for daily requirements. Write an inequality that represents Lawren’s situation.

A man goes 3 kms east from point A and takes right tum from point B to move 4 kms to point c. What is the minimum distance between paint A and point C

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The eccentricity of an ellipse whose centre is at the origin is $1 half space$ If one of its directrices is $x equals negative 4$ then the equation of the normal to it at $open parentheses 1 comma fraction numerator 3 over denominator 2 end fraction close parentheses text end text$ is

The correct answer is: $4 x minus 2 y equals 1$

Use counter to add -5 + 2, where is + and Is –
Start with:
You add:
Which picture shows the sum:

Use counter to add -5 + 2, where is + and Is –
Start with:
You add:
Which picture shows the sum:

Height of 5 students in a classroom are 125 cm,134 cm, 157 cm,110 cm,146 cm.
Find the range of height

Height of 5 students in a classroom are 125 cm,134 cm, 157 cm,110 cm,146 cm.
Find the range of height

These are the first eight ionization energies for a particular neutral atom. All values are expressed in MJ mol^-1. How many valence electrons do/does this atom possess?

1st

2nd

3rd

4th

5th

6th

7th

8th

1.31

3.39

5.30

7.47

10.99

13.33

71.33

84.01

These are the first eight ionization energies for a particular neutral atom. All values are expressed in MJ mol^-1. How many valence electrons do/does this atom possess?

1st

2nd

3rd

4th

5th

6th

7th

8th

1.31

3.39

5.30

7.47

10.99

13.33

71.33

84.01

Polly is measuring the temperature of different chemical mixture. The temperature of two mixtures are shown in table as

Which mixture has highest absolute value

Polly is measuring the temperature of different chemical mixture. The temperature of two mixtures are shown in table as

Which mixture has highest absolute value

Which of the following represents x $greater or equal than$ 4

Which of the following represents x $greater or equal than$ 4