Conic Sections 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 
