Question

find the center and radius of the circle,x2+y2- 8x-4y-5=0

Answer 1

(x² - 8x + 16) + (y² - 4y + 4) = 5+16+4
(x-4)² + (y-2)² = 5²
So, center is (4,2) and radius is 5.

Answer 2

We have,

x² + y² -8x -4y -5 =0

Or x² -8x +y² -4y -5= 0

Or x² -2 × x × 4 + 4² + y² - 2 × y × 2 + 2² - 5 = 0

Or (x-4)² + (y-2)² = 5

Or $\sqrt{(x-4)^2 + (y-2)^2} = \sqrt{5}$, which is the standard eqation of a circle.

Thus,
Radius of the circle = √5
Centre of the circle = (4,2)