NCERT Solutions
Class 11 - Mathematics - Chapter 10: CONIC SECTIONS
EXERCISE 10.2

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Question. 1

For the parabola \(y^2 = 12x\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F (3, 0), axis – x-axis, directrix \(x = -3\), length of latus rectum = 12

Question. 2

For the parabola \(x^2 = 6y\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F \((0, \tfrac{3}{2})\), axis – y-axis, directrix \(y = -\tfrac{3}{2}\), length of latus rectum = 6

Question. 3

For the parabola \(y^2 = -8x\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F (−2, 0), axis – x-axis, directrix \(x = 2\), length of latus rectum = 8

Question. 4

For the parabola \(x^2 = -16y\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F (0, −4), axis – y-axis, directrix \(y = 4\), length of latus rectum = 16

Question. 5

For the parabola \(y^2 = 10x\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F \((\tfrac{5}{2}, 0)\), axis – x-axis, directrix \(x = -\tfrac{5}{2}\), length of latus rectum = 10

Question. 6

For the parabola \(x^2 = -9y\), find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.

Answer:

F \((0, -\tfrac{9}{4})\), axis – y-axis, directrix \(y = \tfrac{9}{4}\), length of latus rectum = 9

Question. 7

Find the equation of the parabola whose focus is (6, 0) and directrix is \(x = -6\).

Answer:

\(y^2 = 24x\)

Question. 8

Find the equation of the parabola whose focus is (0, −3) and directrix is \(y = 3\).

Answer:

\(x^2 = -12y\)

Question. 9

Find the equation of the parabola with vertex (0,0) and focus (3,0).

Answer:

\(y^2 = 12x\)

Question. 10

Find the equation of the parabola with vertex (0,0) and focus (−2,0).

Answer:

\(y^2 = -8x\)

Question. 11

Find the equation of the parabola with vertex (0,0) passing through (2,3) and whose axis is along the x-axis.

Answer:

\(2y^2 = 9x\)

Question. 12

Find the equation of the parabola with vertex (0,0), passing through (5,2) and symmetric with respect to the y-axis.

Answer:

\(2x^2 = 25y\)