NCERT Solutions class-11 Maths Exercise 11.2

Exercise 11.2

In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

1.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are (3, 0).

Axis of parabola is

Equation of the directrix is

Length of latus rectum =

---

2.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are

Axis of parabola is

Equation of the directrix is

Length of latus rectum = = 6

---

3.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are (–2, 0).

Axis of parabola is

Equation of the directrix is

Length of latus rectum =

---

4.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are

Axis of parabola is

Equation of the directrix is

Length of latus rectum =

---

5.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are

Axis of parabola is

Equation of the directrix is

Length of latus rectum = = 10

---

6.

Ans. Given: Equation of parabola

Comparing with we have

Coordinates of focus are

Axis of parabola is

Equation of the directrix is

Length of latus rectum = = 9

---

In each of the following Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions:

7. Focus (6, 0); directrix

Ans. Given: Directrix : and

Axis of parabola is axis.

The required equation of parabola

---

8. Focus directrix

Ans. Given: Directrix: and

Axis of parabola is axis.

The required equation of parabola

---

9. Vertex (0, 0); Focus (3, 0)

Ans. Given: vertex is at (0, 0), and

Axis of parabola is axis.

The required equation of parabola

---

10. Vertex (0, 0); Focus

Ans. Given: vertex is at (0, 0), and

Axis of parabola is axis.

The required equation of parabola

---

11. Vertex (0, 0) passing through (2, 3) and axis is along axis.

Ans. Given: vertex (0, 0) and axis is along axis.

Parabola is of the form

Since the parabola passes through the point (2, 3).

The required equation of parabola

---

12. Vertex (0, 0) passing through (5, 2) and symmetric with respect to axis.

Ans. Given: vertex (0, 0) and axis is along axis.

Parabola is of the form

Since the parabola passes through the point (5, 2).

The required equation of parabola