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Chapter 11 Conic Sections Ex-11.4 Interview Questions Answers

Question 1 : Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 

Answer 1 :

The given equation is.

On comparing this equation with the standardequation of hyperbola i.e.,, we obtain a =4 and b = 3.

We know that a2 + b2 = c2.

Therefore,

The coordinates of thefoci are (±5, 0).

The coordinates of thevertices are (±4, 0).

Lengthof latus rectum

Question 2 : Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 

Answer 2 :

The given equation is.

On comparing this equation with the standardequation of hyperbola i.e., , we obtain a =3 and.

We know that a2 + b2 = c2.

Therefore,

The coordinates of thefoci are (0, ±6).

The coordinates of thevertices are (0, ±3).

Lengthof latus rectum

Question 3 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola9y2 – 4x2 = 36

Answer 3 :

The given equation is 9y2 – 4x2 = 36.

It can be written as

9y2 – 4x2 = 36

On comparing equation (1) with the standardequation of hyperbola i.e.,, we obtain a =2 and b = 3.

We know that a2 + b2 = c2.

Therefore,

The coordinates of thefoci are.

The coordinates of thevertices are.

Lengthof latus rectum

Question 4 :

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola16x2 – 9y2 = 576

Answer 4 :

The given equation is 16x2 – 9y2 = 576.

It can be written as

16x2 – 9y2 = 576

On comparing equation (1) with the standardequation of hyperbola i.e.,, we obtain a =6 and b = 8.

We know that a2 + b2 = c2.

Therefore,

The coordinates of thefoci are (±10, 0).

The coordinates of thevertices are (±6, 0).

Lengthof latus rectum

Question 5 :

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola5y2 – 9x2 = 36

Answer 5 :

The given equation is 5y2 – 9x2 = 36.

On comparing equation (1) with the standardequation of hyperbola i.e.,, we obtain a =  and b = 2.

We know that a2 + b2 = c2.

Therefore, the coordinatesof the foci are.

The coordinates of thevertices are.

Lengthof latus rectum

Question 6 :

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola49y2 – 16x2 = 784

Answer 6 :

The given equation is 49y2 – 16x2 = 784.

It can be written as 49y2 – 16x2 = 784

On comparing equation (1) with the standardequation of hyperbola i.e.,, we obtain a =4 and b = 7.

We know that a2 + b2 = c2.

Therefore,

The coordinates of thefoci are.

The coordinates of thevertices are (0, ±4).

Length of latus rectum

Question 7 : Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Answer 7 :

Vertices (±2, 0), foci(±3, 0)

Here, the vertices are on the x-axis.

Therefore, the equation ofthe hyperbola is of the form .

Since the vertices are (±2, 0), =2.

Since the foci are (±3, 0), c =3.

We know that a2 + b2 = c2.

Thus,the equation of the hyperbola is.

Question 8 : Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Answer 8 :

Vertices (0, ±5), foci (0,±8)

Here, the vertices are on the y-axis.

Therefore, the equation ofthe hyperbola is of the form.

Since the vertices are (0, ±5), =5.

Since the foci are (0, ±8), c =8.

We know that a2 + b2 = c2.

Thus,the equation of the hyperbola is.

Question 9 : Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Answer 9 :

Vertices (0, ±3), foci (0,±5)

Here, the vertices are on the y-axis.

Therefore, the equation ofthe hyperbola is of the form.

Since the vertices are (0, ±3), =3.

Since the foci are (0, ±5), c =5.

We know that a2 + b2 = c2.

32 + b2 = 52

 b2 = 25 – 9 = 16

Thus,the equation of the hyperbola is.

Question 10 : Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Answer 10 :

Foci (±5, 0), thetransverse axis is of length 8.

Here, the foci are on the x-axis.

Therefore, the equation ofthe hyperbola is of the form.

Since the foci are (±5, 0), c =5.

Since the length of the transverse axis is8, 2a = 8  a = 4.

We know that a2 + b2 = c2.

42 + b2 = 52

 b2 = 25 – 16 = 9

Thus,the equation of the hyperbola is.


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Chapter 11 Conic Sections Ex-11.4 Contributors

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