# Parabola (S .N. Dey ) | Ex-4 | Part-5

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 