# Parabola (S .N. Dey ) | Ex-4 | Part-7

##### In the previous article, we have solved few Short answer type questions (5-10) 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.

Show that the locus of the middle points of chords of the parabola passing through the vertex is the parabola

Solution.

One end of the chord is the vertex of parabola, which is  .

Let the mid point of the chords be and the other end of the chord be

Mid-point of is

Find the locus of the middle points of a family of focal chords of the parabola

Solution.

The extremities of the focal chord of the parabola are and

Let the mid-point of the chord be

From and we get,

Hence, the locus of the mid-point of the chord is

is any ordinate of the parabola the point divides in the ratio Find the locus of

Solution.

Let be any point on the parabola and be the ordinate of the parabola.

Again, let divides in the ratio

the locus of the point is

Prove that the lines joining the ends of latus rectum of the parabola with the point of intersection of its axis and directrix are at right angles.

Solution.

Let be the focus and be the length of the latus rectum of length unit of the parabola

The directrix of the parabola and the axis of the parabola

So, the point of intersection of the directrix and the axis of the parabola is

Slope of is

Slope of is

So,

Hence,

Prove that the lines joining the ends of latus rectum of the parabola The ordinate of is twice that of Prove that the locus of the mid-point of is

Solution.

Let

By question,

Now, since lies on the parabola ,

Let be the mid-point of

By , we get

Hence, the locus of is