Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas  49y2 – 16x2 = 784.

Asked by Pragya Singh | 1 year ago |  136

#### 1 Answer

##### Solution :-

The equation is 49y2 – 16x2 = 784.

Let us divide the whole equation by 784, we get

$$\dfrac{49y^2}{784}- \dfrac{16x^2}{784}$$

$$\dfrac{784}{784}$$

$$\dfrac{y^2}{16}- \dfrac{x^2}{49}=1$$

On comparing this equation with the standard equation of hyperbola

$$\dfrac{y^2}{a^2}- \dfrac{x^2}{b^2}=1$$

We get a = 4 and b = 7,

It is know that, a2 + b2 = c2

So,

c2 = 16 + 49

c2 = 65

c = $$\sqrt{65}$$

Then,

The coordinates of the foci are (0,$$\sqrt{65}$$) and (0, –$$\sqrt{65}$$).

The coordinates of the vertices are (0, 4) and (0, -4).

Eccentricity, e = $$\dfrac{c}{a}$$$$\dfrac{\sqrt{65}}{4}$$

Length of latus rectum = $$\dfrac{2b^2}{a}$$

$$\dfrac{(2×7^2)}{4}$$

$$\dfrac{(2×49)}{4}$$

$$\dfrac{49}{2}$$

Answered by Abhisek | 1 year ago

### Related Questions

#### An equilateral triangle is inscribed in the parabola y2 = 4ax,

An equilateral triangle is inscribed in the parabola y2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Class 11 Maths Conic Sections View Answer

#### A man running a racecourse notes that the sum of the distances from the two flag posts from him is always

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Class 11 Maths Conic Sections View Answer

#### Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Class 11 Maths Conic Sections View Answer

#### A rod of length 12 cm moves with its ends always touching the coordinate axes.

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Class 11 Maths Conic Sections View Answer

#### An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Class 11 Maths Conic Sections View Answer