# Math Help - Analytic Geometry Homework

1. ## Analytic Geometry Homework

Well I'm kinda stumped and I need you guys...

1.) The length of a diameter of a circle described by 9x^2 + 9y^2 = 16 is?

2.) Find the equation of the circle with center on x+y = 4 and 5x+2y+1=0 and having a radius of 3.

2. Originally Posted by valcross
Well I'm kinda stumped and I need you guys...

1.) The length of a diameter of a circle described by 9x^2 + 9y^2 = 16 is?

1)

$9x^2 + 9y^2 = 16$
$x^2 + y^2 = \frac{16}{9}$
As general form is $x^2 + y^2 = r^2$
$\implies r^2 = \frac{16}{9}$
$r = \frac{4}{3}$
Diameter is two times radius.
$\therefore d=\frac{8}{3}$

3. Regarding #2:

The equation for a circle with center (h,k) and radius r is:

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

So you know r = 3. Where's the center?

Recall that it lies on the two lines given, so find the intersection of the two lines. I did it by substitution, starting with the first equation, which gives:

$y=4-x$.

Sub this into the other equation for y, which gives:

$5x+8-2x+1=0$

$3x+9=0$

$3x=-9$

$x=-3$.

Recall $y=4-x$, so $y=4-(-3)=7$.

So your center is at $(-3,7)$. Now you know h, k, and r, the three essentials for writing the equation of a circle.

There you are!

4. Thanks guys, that was very educational, not to mention I now have my homework done thanks to you.