CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 11 – Conic Section Maths
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From equation (2), we obtain
h 2 + b 2 ‒’ 2bk + k 2 = h 2 + k 2
⇒ b 2 –2bk = 0
⇒ b(b – 2k) = 0
⇒ b = 0 or (b – 2k) = 0
However, b ≠ 0; hence, (b –2k) = 0 ⇒ k = 2
b .
Thus, the equation of the required circle is
2 2 2 2
a b a b
x y
2
2
2
2
2 2 2 2
2x a 2y b a b
2
2
4
4x 4ax a 4y 4by b a b
2 2 2 2 2 2
2 2
4x 4y 4ax 4by
0
2 2
x y ax by
0
Question 14:
Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).
Solution 14:
The centre of the circle is given as (h, k) = (2, 2).
Since the circle passes through point (4, 5), the radius (r) of the circle is the distance between
the points (2, 2) and (4, 5).
2 2 2 2
r
24 25 2 3 49 13
Thus, the equation of the circle is
x h y k r
2 2 2
2 2
x 2 y 2 13
2 2
x x y y
4 4 4 4 13
2 2
x y x y
4 4 5 0
2
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