Question

The equation of a circle is `x^2+y^2-4x+10y = -20`, what are the co-ordinates of the center and the length of the radius of the circle?

Answer 1

centre = (2 , - 5 ) and radius = 3

Explanation:

The general form of the equation of a circle is:

`x^2 + y^2 + 2gx + 2fy + c = 0`

in this question : `x^2 + y^2 - 4x + 10y + 20 = 0`

comparing the coefficients : 2g = - 4 `rArr g = - 2`

`2f = 10 rArr f = 5 and c = 20`

centre = ( - g , - f ) = (2 , - 5 )

and `r = sqrt(g^2 + f^2 - c ) = sqrt((-2)^2 + 5^2 - 20 )`

`rArr r = sqrt(4 + 25 - 20 ) = sqrt9 = 3`