The equation of a circle is given by (x^{2} + y^{2} – 4x – 2y…

The equation of a circle is given by (x^{2} + y^{2} – 4x – 2y – 3). Find the radius and the coordinates of its centre.

Correct Answer: Option C

Explanation

Equation of a circle with radius r and centre (a, b).

= ((x – a)^{2} + (y – b)^{2} = r^{2})

Expanding, we have

(x^{2} – 2ax + a^{2} + y^{2} – 2by + b^{2} = r^{2})

Comparing, with (x^{2} + y^{2} – 4x – 2y – 3 = 0)

(2a = 4 implies a = 2)

(2b = 2 implies b = 1)

(r^{2} – a^{2} – b^{2} = 3 implies r^{2} = 3 + 2^{2} + 1^{2} = 8)

(r = 2sqrt{2})