Question

Can you please help graph the equation?

Answer 1

See explanation

Explanation:

Equation for a circle uses Pythagoras.

Case 1: centre at origin:`x^2+y^2=r^2 larr" A triangle"`

Case 2: centre at `(a,b)->(x-a)^2+(y-b)^2=r^2`

For case 2 what you are doing is 'hypothetically' moving the centre back to the origin.

`color(blue)("Centre (2,-1) radius 4")`

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

`color(blue)("Centre (-3,4) has point (2,2)")`

We need the distance from the centre to the point

Again we use Pythagoras and the differences in `x and y`

So we have: `r=sqrt( [2-(-3)]^2+[2-4 ]^2)`

`color(white)("ddddddddd")r^2=color(white)("dddd")5^2+(-2)^2color(white)("dddddd")=color(white)("d")29`

So the equation for this circle is:

`(x-a)^2+(y-b)^2=r^2`

`[x-(-3)]^2+[y-4]^2=29`

`color(white)("dd")[x+3]^2color(white)("dd")+[y-4]^2=29`