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Class 11-science NCERT Solutions Maths Chapter 10 - Conic Sections

Conic Sections Exercise Ex. 10.1

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Conic Sections Exercise Ex. 10.2

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Conic Sections Exercise Ex. 10.3

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Conic Sections Exercise Ex. 10.4

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Vertices (0, ± 3), foci (0, ± 5)

Here, the vertices are on the y-axis.

begin mathsize 12px style therefore the space equation space of space the space hyperbola space is space of space the space form space straight y squared over straight a squared minus straight x squared over straight b squared equals 1. end style

Since the Vertices are (0, ± 3), a = 3

Since the foci are (0, ± 5), c = 5

We know that a+ b2 = c2

∴ 32 + b2 = 52

∴ b2 = 25 - 9 = 16

begin mathsize 12px style therefore the space equation space of space the space hyperbola space is space of space the space form space straight y squared over 9 minus straight x squared over 16 equals 1. end style

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Conic Sections Exercise Misc. Ex.

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Solution 7

 

Let A and B the positions of the two flag posts and P(x, y) be the position of the man.

Accordingly, PA + PB = 10

We know that if a point moves in a plane in such a way that the sum of its distances from two fixed points is constant, then the path is an ellipse and this constant value is equal to the length of the major axis of the ellipse.

Therefore, the path described by the man is an ellipse where the length of the major axis is 10 m, while points A and B are the foci.

Taking the origin of the co-ordinate plane as the centre of the ellipse, while taking the major axis along the x-axis, the ellipse can be diagrammatically represented as

Solution 8


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