# 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) ofÂ 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