Find the area of the circle whose equation is given as (x^{2} + y^{2} -…

Find the area of the circle whose equation is given as (x^{2} + y^{2} – 4x + 8y + 11 = 0).

Correct Answer: Option C

Explanation

Equation of a circle: ((x – a)^{2} + (y – b)^{2} = r^{2})

Given that (x^{2} + y^{2} – 4x + 8y + 11 = 0)

Expanding the equation of a circle, we have: (x^{2} – 2ax + a^{2} + y^{2} – 2by + b^{2} = r^{2})

Comparing this expansion with the given equation, we have

(2a = 4 implies a = 2)

(-2b = 8 implies b = -4)

(r^{2} – a^{2} – b^{2} = -11 implies r^{2} = -11 + 2^{2} + 4^{2} =9)

(r = 3)

(Area = pi r^{2} = pi times 3^{2})

= (9pi)