Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4x2 + 9y2 = 36

Asked by Pragya Singh | 11 months ago |  79

#### 1 Answer

##### Solution :-

The equation is 4x2 + 9y2 = 36

or $$\dfrac{x^2}{9}$$ + $$\dfrac{y^2}{4}$$ = 1 or $$\dfrac{x^2}{3^2}$$+ $$\dfrac{y^2}{2^2}$$ = 1

Here, the denominator of $$\dfrac{x^2}{3^2}$$ is greater than the denominator of $$\dfrac{y^2}{2^2}$$.

So, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation with

$$\dfrac{x^2}{a^2}$$ +$$\dfrac{y^2}{b^2}$$ = 1, we get

a =3 and b =2.

c = $$\sqrt{ (a^2 – b^2)}$$

$$\sqrt{ (9– 4)}$$

=$$\sqrt{5}$$

Then,

The coordinates of the foci are ($$\sqrt{5}$$, 0) and ($$-\sqrt{5}$$, 0).

The coordinates of the vertices are (3, 0) and (-3, 0)

Length of major axis = 2a = 2 (3) = 6

Length of minor axis = 2b = 2 (2) = 4

Eccentricity, e = $$\dfrac{c}{a}$$$$\dfrac{\sqrt{5}}{3}$$

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

= $$\dfrac{(2×2^2)}{3}$$ = $$\dfrac{(2×4)}{3}$$$$\dfrac{8}{3}$$

Answered by Abhisek | 11 months 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