How do you write the equation of the circle in standard form? and what is the center and radius of it?
$\displaystyle 4x^2 + 4y^2 + 24x + 16y + 43 = 0$
A step-by-step view would really help to understand for future problems.
Thanks!
How do you write the equation of the circle in standard form? and what is the center and radius of it?
$\displaystyle 4x^2 + 4y^2 + 24x + 16y + 43 = 0$
A step-by-step view would really help to understand for future problems.
Thanks!
I will continue from here $\displaystyle 4(x^2 + 6x) + 4(y^2 + 4y) + 43 = 0$ (*)
$\displaystyle x^2+6x=x^2+6x+9-9=(x+3)^2 -9$ (1)
$\displaystyle y^2+4y=y^2+4y+4-4=(y+2)^2-4$ (2)
Substitute (1) and (2) into (*):
you get $\displaystyle 4*(x+3)^2-4*9+4*(y+2)^2-4*4+43=4(x+3)^2+4(y+2)^2=9$ Center is at $\displaystyle x=-3$ and $\displaystyle y=-2$ ,Radius is 3
$\displaystyle
4x^2 + 4y^2 + 24x + 16y + 43 = 0
$
Rearrange the equation:
$\displaystyle 4x^2 + 24x + 4y^2 + 16y = -43$
Try and make two perfect squares on the left side of the eqn.
$\displaystyle 4x^2 + 24x + 36 + 4y^2 + 16y + 16 = -43 + 36 + 16$
$\displaystyle (2x+6)^2 + (2y+4)^2 = 9$
Then find the centre and radius of the circle
Oh! Thank you. I forgot that the equation was like this $\displaystyle (x - h)^2 + (y - k)^2 = r^2$
meaning that since it was a positive, it is a negative then...
I didn't read the insulting post, but if it was something like how can I make such a simply mistake and saying how stupid I am, then I don't care because I'm too young to understand this stuff fully anyways...
I'm only in the 8th grade...