Question

X^2 +y^2-6x+2y+9=0 find the h,k Find the radius of circleFind the interceptsGraph the circle

Answer 1

The standard equation of a circle can be wriiten as;

`(x-h)^2+(y-k)^2=r^2`

So, to get the value of h,k and r we need to express the given equation in this form.

The equation is given as;

`x^2+y^2-6x+2y+9=0`

Then we will try to express this equation in the standard equation of circle form.

`x^2-6x+9+y^2+2y+1=1`

Note that we added 1 to both sides so that we can factorise the equation.

Factorizing, we have;

`(x-3)^2+(y+1)^2=1`

Then finally we have;

`(x-3)^2+(y-(-1))^2=1^2`

Comparing the equation to the standard form we have;

`\begin{gathered} h=3 \\ k=-1 \\ radius\rightarrow r=1 \end{gathered}`

Then lastly we need to graph the equation;

From the graph, we can see that the only intercept we have is at;

`\begin{gathered} x=3 \\ \text{ point }\rightarrow(3,0) \end{gathered}`

There is no intercept on the y axis.