Chapter 11 Conic Sections Ex-11.1 |
Chapter 11 Conic Sections Ex-11.2 |
Chapter 11 Conic Sections Ex-11.3 |

**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 *a*^{2} + *b*^{2} = *c*^{2}.

Therefore,

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

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

Lengthof latus rectum

**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 *a*^{2} + *b*^{2} = *c*^{2}.

Therefore,

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

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

Lengthof latus rectum

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola9*y*^{2} – 4*x*^{2} = 36

**Answer
3** :

The given equation is 9*y*^{2} – 4*x*^{2} = 36.

It can be written as

9*y*^{2} – 4*x*^{2} = 36

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

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Therefore,

The coordinates of thefoci are.

The coordinates of thevertices are.

Lengthof latus rectum

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola16*x*^{2} – 9*y*^{2} = 576

**Answer
4** :

The given equation is 16*x*^{2} – 9*y*^{2} = 576.

It can be written as

16*x*^{2} – 9*y*^{2} = 576

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

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Therefore,

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

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

Lengthof latus rectum

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola5*y*^{2} – 9*x*^{2} = 36

**Answer
5** :

The given equation is 5*y*^{2} – 9*x*^{2} = 36.

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

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Therefore, the coordinatesof the foci are.

The coordinates of thevertices are.

Lengthof latus rectum

Find the coordinates of the foci and thevertices, the eccentricity, and the length of the latus rectum of the hyperbola49*y*^{2} – 16*x*^{2} = 784

**Answer
6** :

The given equation is 49*y*^{2} – 16*x*^{2} = 784.

It can be written as 49*y*^{2} – 16*x*^{2} = 784

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

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Therefore,

The coordinates of thefoci are.

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

Length of latus rectum

**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), *a *=2.

Since the foci are (±3, 0), *c* =3.

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Thus,the equation of the hyperbola is.

**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), *a *=5.

Since the foci are (0, ±8), *c* =8.

We know that *a*^{2} + *b*^{2} = *c*^{2}.

Thus,the equation of the hyperbola is.

**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), *a *=3.

Since the foci are (0, ±5), *c* =5.

We know that *a*^{2} + *b*^{2} = *c*^{2}.

∴3^{2} + *b*^{2} = 5^{2}

⇒ *b*^{2} = 25 – 9 = 16

Thus,the equation of the hyperbola is.

**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, 2*a* = 8 ⇒ *a* = 4.

We know that *a*^{2} + *b*^{2} = *c*^{2}.

∴4^{2} + *b*^{2} = 5^{2}

⇒ *b*^{2} = 25 – 16 = 9

Thus,the equation of the hyperbola is.

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