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A day full of math games & activities. Find one near you.
Find the centre and radius of the circle x2 + y2 - 4x - 8y - 45 = 0
Solution:
The equation of the given circle is
x2 + y2 - 4x - 8y - 45 = 0
⇒ x2 + y2 - 4x - 8y - 45 = 0
⇒ (x2 - 4x) + (y2 - 8y) = 45
⇒ {x2 - 2(x)(2) + 22} + {y2 - 2 (y )(4) + 42} - 4 - 16 = 45
⇒ ( x - 2)2 + (y - 4)2 = 65
⇒ ( x - 2)2 + ( y - 4)2 = (√65)2
which is of the form (x - h)2 + (y - k)2 = r2
Therefore, on comparing both equations we get
h = 2, k = 4 and r = √65
Thus, the centre of the given circle is (2, 4) while its radius is √ 65
NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.1 Question 7
Find the centre and radius of the circle x2 + y2 - 4x - 8y - 45 = 0
Summary:
The center and radius of the circle are (2, 4) and √ 65 respectively
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