Good morning forum I need some assistance with the following question:
Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.
Thanks AC
Good morning forum I need some assistance with the following question:
Put the equation x2 + y2 + 8x + 2y = 29 into standard form and sketch the graph of the equation.
Thanks AC
I take it that the 2's are superscript.
So it should read $\displaystyle x^2 + y^2 + 8x + 2y = 29$.
First off, this is the equation of a circle.
The standard form of a circle is $\displaystyle (x - h)^2 + (y - k)^2 = r^2$ where h is the x-coordinate of the centre, k is the y-coordinate of the centre, and r is the radius.
To get it into this standard form, complete the square on the x terms and the y terms.
$\displaystyle x^2 + 8x + y^2 + 2y = 29$
$\displaystyle x^2 + 8x + 4^2 + y^2 + 2y + 1^2 = 29 + 4^2 + 1^2$
$\displaystyle (x + 4)^2 + (y + 1)^2 = 46$
$\displaystyle [x - (-4)]^2 + [y - (-1)]^2 = (\sqrt{46})^2$.
So what's the centre? What's the radius? Can you sketch the circle?
You have to complete squares, 8th grade trick.
$\displaystyle x^2+8x=(x+4)^2-16$ and $\displaystyle y^2+2y=(y+1)^2-1$
substituting this and rearranging the following is obtained:
$\displaystyle (x+2)^2+(y+1)^2=29+16+1=46$
this is a circle with center at $\displaystyle (-2,-1)$ and radius $\displaystyle \sqrt{46}$