In the previous article, we have solved few Short answer type questions of Parabola Chapter . In this article, we have solved Short answer type questions of Parabola Chapter (Ex-4) of S.N.Dey mathematics, Class 11.

Find the equation of the parabola whose vertex is at , axis is parallel to axis and length of the latus rectum is

Solution.

We know that the equation of the parabola with the vertex can be written as where is the length of the latus rectum and the axis of the parabola is parallel to axis.

Here,

Hence, the required equation of the parabola is

The co-ordinates of the vertex and focus of a parabola are and respectively; find its equation.

Solution.

Here, Vertex . Clearly the focus and vertex of the parabola lie on which is parallel to axis.

Since the focus lies on the left side of the vertex, the equation of the parabola is

Here,

So, the required equation of the parabola is

Show that the equation of the parabola whose vertex is and focus is is

Solution.

Here, Vertex . Clearly the focus and vertex of the parabola lie on which is parallel to axis.

Since the focus lies below the vertex, the equation of the parabola is

Here,

So, the required equation of the parabola is

Show that the equation of the parabola whose vertex and focus are on the axis at distances and from the origin respectively is

Solution.

Clearly, the vertex of the parabola Again, the vertex and focus of the parabola lie on the axis . So, the axis of the parabola lies along the axis.

Now, the equation of the parabola can be written as

where is the length of the latus rectum.

By question,

So, by and we can write the equation of the parabola as

Now,

Case-1 :

Now, if , focus lies on the left side of the vertex of the parabola.

the equation of the parabola

Case-2 :

Again, for , focus lies on the right side of the vertex of the parabola.

Hence, for both cases, the equation of the parabola is

Find the equation of the parabola whose vertex is the point and directrix is the line

Solution.

The directrix of the parabola is the line which is parallel to the axis. So, the axis of the parabola is parallel to axis.

Again, since the vertex of the parabola is on the right side of the directrix, the equation of the parabola can be written as

Now,

Hence, the equation of the required parabola is

Find the equation of the parabola whose vertex is the point and the equation of directrix is

Solution.

The equation of the directrix is The co-ordinates of the vertex is

So, the equation of the parabola is