Real life examples of parabola, Standard forms of Parabola, Definition and geometric proof for parabola, Derivation for equation of parabola, Way to remember all rules of parabolas, Derivation for length of latus rectum of parabola

 NCERT 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.

Question 1. $y^2 = 12x$

Question 2. $x^2 = 6y$

Question 3. $y^2 = -8x$

Question 4. $x^2=-16y$

Question 5. $y^2 = 10x$

Question 6. $x^2=-9y$

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

Question 7. Focus (6,0); directrix x = – 6

Question 8. Focus (0,–3); directrix y = 3

Question 9. Vertex (0, 0); focus (3, 0)

Question 10. Vertex (0, 0); focus (–2, 0)

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

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

 MISCELLANEOUS EXERCISE

Question 1.If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Question 2. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Question 3.The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.