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Question

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

$\frac{a^{2}}{m^{2}} + \frac{b^{2}}{l^{2}} = \frac{(a^{2} - b^{2})}{n^{2}}$
$\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}} = \frac{{(a^{2} - b^{2})}^{2}}{n^{2}}$
$\frac{a^{2}}{l^{2}} - \frac{b^{2}}{m^{2}} = \frac{{(a^{2} - b^{2})}^{2}}{n^{2}}$
None of these

The correct answer is: $fraction numerator a to the power of 2 end exponent over denominator l to the power of 2 end exponent end fraction plus fraction numerator b to the power of 2 end exponent over denominator m to the power of 2 end exponent end fraction equals fraction numerator open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses to the power of 2 end exponent over denominator n to the power of 2 end exponent end fraction$

The equation of any normal to $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 text is end text$
$a x s e c invisible function application theta minus b y c o s e c invisible function application theta equals a to the power of 2 end exponent minus b to the power of 2 end exponent$
The straight line
$∣ x plus m y plus n equals 0$
$text is a normal to the ellipse end text fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 text if Eqs. end text left parenthesis 1 right parenthesis text and end text left parenthesis 2 right parenthesis text repre end text$ sent the same line. Then
$fraction numerator a s e c invisible function application theta over denominator I end fraction equals fraction numerator b c o s e c invisible function application theta over denominator negative m end fraction equals fraction numerator a to the power of 2 end exponent minus b to the power of 2 end exponent over denominator negative n end fraction$
$rightwards double arrow c o s invisible function application theta equals fraction numerator negative a n over denominator I open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses end fraction$
$text and end text s i n invisible function application theta equals fraction numerator b n over denominator m open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses end fraction$
$text Since end text c o s to the power of 2 end exponent invisible function application theta plus s i n to the power of 2 end exponent invisible function application theta equals 1 comma text we get end text$
$table row cell fraction numerator a to the power of 2 end exponent n to the power of 2 end exponent over denominator 1 to the power of 2 end exponent open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses to the power of 2 end exponent end fraction plus fraction numerator b to the power of 2 end exponent n to the power of 2 end exponent over denominator m open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses to the power of 2 end exponent end fraction equals 1 end cell row cell rightwards double arrow fraction numerator a to the power of 2 end exponent over denominator l to the power of 2 end exponent end fraction plus fraction numerator b to the power of 2 end exponent over denominator m to the power of 2 end exponent end fraction equals fraction numerator open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses to the power of 2 end exponent over denominator n to the power of 2 end exponent end fraction end cell end table$

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.

Maths-General

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

General

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?

Maths-General

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

Maths-General

General

Maths-

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

Maths-General

General

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.

Maths-General

General

Maths-

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

Maths-General

General

Maths-

Which of the following is correct:

Maths-General

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

General

Maths-

The more time people spend using social media, the less they read books. Identify the independent variable.

Maths-General

General

Maths-

While solving math problems one of the group calculator and the other did manually. First group which used calculator was able to complete the assignment early. What is dependent variable

Maths-General

General

Maths-

Nine workers could finish the work in five days, whereas 6 workers do the same work in 8 days. Identify the independent variable

Maths-General

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The line is a normal to the ellipse is

None of these

The correct answer is:

The equation of any normal to The straight line sent the same line. Then

Related Questions to study

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.

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.

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

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?

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?

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

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

Which of the following represents x 4

Which of the following represents x 4

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

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

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.

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.

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

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

Which of the following is correct:

Which of the following is correct:

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

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

The more time people spend using social media, the less they read books. Identify the independent variable.

The more time people spend using social media, the less they read books. Identify the independent variable.

While solving math problems one of the group calculator and the other did manually. First group which used calculator was able to complete the assignment early. What is dependent variable

While solving math problems one of the group calculator and the other did manually. First group which used calculator was able to complete the assignment early. What is dependent variable

Nine workers could finish the work in five days, whereas 6 workers do the same work in 8 days. Identify the independent variable

Nine workers could finish the work in five days, whereas 6 workers do the same work in 8 days. Identify the independent variable

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$\frac{a^{2}}{m^{2}} + \frac{b^{2}}{l^{2}} = \frac{(a^{2} - b^{2})}{n^{2}}$
$\frac{a^{2}}{l^{2}} + \frac{b^{2}}{m^{2}} = \frac{{(a^{2} - b^{2})}^{2}}{n^{2}}$
$\frac{a^{2}}{l^{2}} - \frac{b^{2}}{m^{2}} = \frac{{(a^{2} - b^{2})}^{2}}{n^{2}}$
None of these

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