# Parabola (S .N. Dey ) | Ex-4 | Part-2

In the previous article , we have solved 6 Long Answer Type Questions of Parabola Chapter. In this article, we have solved 6 more Long answer type questions of Parabola Chapter (Ex-4) of S.N.Dey mathematics, Class 11. Show that the product of the ordinates of the ends of a focal chord of the parabola is constant.

Solution.

We know that the co-ordinates of extremities of the focal chord are and So, the product of the ordinates  If a straight line passing through the focus of the parabola intersects the parabola at the points and then prove that, Solution.

Let Since the chord of the given parabola passes through the focus i.e., the chord is the focal chord.

So,   Find the equation of the circle passing through the origin and the foci of the parabolas and Solution.

The given equations of parabolas are The focus of the parabola is and that of is Let the equation of the circle be Since the circle passes through the points , so Hence, the equation of the required circle is  Find the equation of the circle on as diameter, where is the focus of and is the centre of Also find the length of the chord of the circle lying along the axis.

Solution.

The co-ordinates of the focus of the parabola are The centre of the given circle is Now, the equation of the circle having diameter with extremities and is So, the length of the chord of the circle lying along the axis is  is any point on the parabola is the ordinate of and is the mid-point of Prove that the locus of is a parabola whose latus rectum is one-fourth that of the given parabola.

Solution.

Let be any point on the parabola Since is the ordinate of Also, let where is the mid-point of  From we get The locus of is which represents the equation of a parabola.

The length of the latus rectum One-fourth the length of the given parabola. Find the equation of the circle drawn on the line-segment joining the foci of the two parabolas and as diameter.

Solution.

The focus of the parabola is and the focus of the parabola is Now the equation of the circle drawn on the line-segment joining the foci and is 