Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x2 = 6y

Asked by Sakshi | 1 year ago |  65

##### Solution :-

Given:

The equation is x2 = 6y

Here we know that the coefficient of y is positive.

So, the parabola opens upwards.

On comparing this equation with x2 = 4ay, we get,

4a = 6

a = $$\dfrac{6}{4}$$

$$\dfrac{3}{2}$$

Thus, the co-ordinates of the focus = (0,a) = (0,$$\dfrac{3}{2}$$)

Since, the given equation involves x2, the axis of the parabola is the y-axis.

The equation of directrix, y =-a, then,

y =$$\dfrac{-3}{2}$$

Length of latus rectum = 4a = 4($$\dfrac{3}{2}$$) = 6

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.