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