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# NCERT Solutions class-11 Maths Exercise 11.2

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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

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