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 $$\dfrac{ x^2}{25} + \dfrac{y^2}{100} = 1$$

Asked by Aaryan | 1 year ago |  52

##### Solution :-

Given:

The equation is $$\dfrac{x^2}{25} + \dfrac{y^2}{100} = 1$$

Here, the denominator of $$\dfrac{y^2}{100}$$ is greater than the denominator of $$\dfrac{x^2}{25}$$.

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

b = 5 and a =10.

c = $$\sqrt{(a^2 – b^2)}$$

= $$\sqrt{(100-25)}$$

$$\sqrt{75}$$

$$5\sqrt{3}$$

Then,

The coordinates of the foci are (0,$$5\sqrt{3}$$) and (0, $$- 5\sqrt{3}$$).

The coordinates of the vertices are (0,$$\sqrt{10}$$) and (0, $$- \sqrt{10}$$)

Length of major axis = 2a = 2 (10) = 20

Length of minor axis = 2b = 2 (5) = 10

Eccentricity, e = $$\dfrac{c}{a}$$ =$$\dfrac{5\sqrt{3}}{10}=\sqrt{\dfrac{3}{2}}$$

Length of latus rectum = $$\dfrac{ 2b^2}{a} =\dfrac{ (2×5^2)}{10}=5$$

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.