In the previous article , we have solved few VSA type questions of Hyperbola chapter of S.N.Dey mathematics, Class 11. In this article , we will solve few more questions of Hyperbola related problems.

9(i) If the length of latus rectum of a rectangular hyperbola is unit, find its equation.
Solution.
The length of the latus rectum is
For rectangular hyperbola,
So, from we get,
Hence, the equation of the rectangular hyperbola is given by
(ii) Find the co-ordinates of the foci of the rectangular hyperbola
Solution.
Comparing the given hyperbola with
we get,
Also, we know that the eccentricity
of any rectangular hyperbola is
The co-ordinates of the foci is given by
10. If the latus rectum and the transverse axis of a hyperbola are equal, show that it is a rectangular hyperbola.
Solution.
We know that the length of latus rectum of the hyperbola is
unit and the transverse axis is given by
unit.
By question,
Hence, by we get,
So, the given hyperbola is a rectangular hyperbola.
11. Find the positions of the points with respect to the hyperbola
Solution(i)
We know that the point lies outside, on or inside the hyperbola
according as
The given equation of the hyperbola can be written as
Now, for the point we get,
Hence, by and
we can conclude that the point
lies inside the given hyperbola.
Solution(ii)
We know that the point lies outside, on or inside the hyperbola
according as
The given equation of the hyperbola can be written as
Now, for the point we get,
Hence, by and
we can conclude that the point
lies inside the given hyperbola.
Solution(iii)
We know that the point lies outside, on or inside the hyperbola
according as
The given equation of the hyperbola can be written as
Now, for the point we get,
Hence, by and
we can conclude that the point
lies outside the given hyperbola.
12. Find the position of the point with respect to the hyperbola
Solution.
We know that the point lies outside, on or inside the hyperbola
according as
The given equation of the hyperbola can be written as
Now, for the point we get,
Hence, by and
we can conclude that the point
lies inside the given hyperbola.
13. Show that the locus of the point of intersection of the lines and
being a variable parameter, is a hyperbola.
Solution.
The given equations of straight lines are
From and
we get,
Hence, by we can conclude that the locus of point of intersection of the given lines is a hyperbola.
14. Find the parametric co-ordinates of the point on the hyperbola
Solution.
The equation of the hyperbola can be written as
Comparing with
we get,
So, we can say that the any point on the hyperbola can be written in parametric form as
By question,
Hence, the parametric co-ordinates of the given point can be written as