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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