Question

Can you help me please, please answer seriously, no links please​

Answer 1

Centre:
`((1)/(2) ,2)`

Radius =
`2`

Explanation:

General formula for a circle:
`(x-a)^2+(y-b)^2=r^2`, where
`r=` the radius of the circle and
`(a,b)` is the centre of the circle.

To find the centre and radius of the circle we should re-write the given equation in the form of the general formula.

So, put the terms with the same variables together:

`4x^2-4x+4y^2+16y+1=0`

We can see that there is a common factor of
`4`, so let's simplify by dividing by
`4`:

`x^2-x+y^2+4y+(1)/(4) =0`

Here we can get it into the general formula by completing the square.

We do this by turning a quadratic with form
`ax^2+bx+c=0` into the form
`(x-d)^2-e+c=0`, where d is half of the coefficient of
`x`, e is
`d^2` and c is the constant of the quadratic.

So let's re-write the equation of the circle:

`(x-(1)/(2) )^2-(1)/(4) +(y-2)^2-4+(1)/(4) =0`

Simplify:
`(x-(1)/(2) )^2 +(y-2)^2-4} =0`

Now we can see that it's very similar to the general equation and all we have to do is bring the
`4` over to the right side.

`(x-(1)/(2) )^2 +(y-2)^2} =4`

So, now we can find the radius and centre.

`(a,b) = ((1)/(2) ,2)`

`r^2=4, r=2`