CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 11 – Conic Section Maths
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The equation of the semi-ellipse will be of the form
axis
Accordingly, 2a = 8 ⇒ a = 4
b = 2
x
a
y
b
2 2
1
2 2
y 0, where a is the semi-major
2 2
x y
Therefore, the equation of the semi-ellipse is 1, y 0 ….(1)
16 4
Let A be a point on the major axis such that AB = 1.5 m.
Draw AC⊥ OB.
OA = (4 – 1.5) m = 2.5 m
The x-coordinate of point C is 2.5.
On substituting the value of x with 2.5 in equation (1), we obtain
2 2
2.5 y
1
16 4
2
6.25 y
1
16 4
2 6.25
y 41
16
2 9.27
y
4 16
2
y
2.4375
y = 1.56 (approx.)
∴AC = 1.56 m
Thus, the height of the arch at a point 1.5 m from one end is approximately 1.56 m.
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