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