Given the circumference of equation \bf{x^(2)+y^(2)-2x+4y-4=0}, find the center and the radius.

Question

Given the circumference of equation
`\bf{x^(2)+y^(2)-2x+4y-4=0}`, find the center and the radius.

Answer 1

We will convert the general equation to the ordinary form \left
`\bf{( x-h \right )^(2)+\left ( y-k \right )^(2)=r^(2)}`; For this we follow the following steps:

We rewrite the equation by ordering the x and y and we complete the perfect square trinomials:

`\bf{x^(2)-2x+1+y^(2)+4y+4=4+1+4 }`

Factor the perfect square trinomials:

`\bf{(x-1)^(2)+(y+2)^(2)=9 }\\\bf{ \ \ \ \ \Rightarrow \ C(1,-2) y \ r=3 }`