Question

Question 7 Find the centre and radius of the circle x^2 + y^2 – 4x – 8y – 45 = 0

Class X1 - Maths -Conic Sections Page 241

Answer 1

concept :- Let standard equation of circle is x² + y² + 2gx + 2fy + C = 0.
Then,
Centre of circle : (-g, -f)
Radius of circle : √(g² + f² - C)


Here, equation of circle is
x² + y² - 4x - 8y - 45 = 0
x² + y² + 2(-2)x + 2(-4)y +(-45) = 0

Centre of circle = (2, 4)
radius of circle = √{2² + 4² - (-45)}
= √(4 + 16 + 45)
= √65