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 $$\dfrac{x^2}{16 }+ \dfrac{y^2}{9} = 1$$

Asked by Aaryan | 1 year ago |  74

##### Solution :-

Given:

The equation is $$\dfrac{ x^2}{16} + \dfrac{y^2}{9} = 1$$

Here, the denominator of $$\dfrac{ x^2}{16}$$ is greater than the denominator of $$\dfrac{ y^2}{9}$$.

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

a = 4 and b = 3.

c = $$\sqrt{(a^2 – b^2)}$$

= $$\sqrt{(16-9)}$$

$$\sqrt{7}$$

Then,

The coordinates of the foci are ($$\sqrt{7}$$, 0) and ($$- \sqrt{7}$$, 0).

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

Length of major axis = 2a = 2 (4) = 8

Length of minor axis = 2b = 2 (3) = 6

Eccentricity, e = $$\dfrac{c}{a}$$ = $$\sqrt{\dfrac{7}{4}}$$

Length of latus rectum = $$\dfrac{2b^2}{a} = \dfrac{(2×3^2)}{4}$$

$$\dfrac{9}{2}$$

Answered by Aaryan | 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.

#### 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.

#### 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.